Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation.
Answers
When a function is plotted on a graph, the domain and the range of the function are the x-coordinate and the y-coordinate respectively.
The domain and the range of the given function are:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex](3,\infty)[/tex]
The given function is:
[tex]g(x) = 3^x + 3[/tex]
First, we plot the graph of g(x)
To do this, we need to generate values for x and g(x). The table is generated as follows:
[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]
[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]
[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]
[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]
[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]
The generated values in tabular form are:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]
Refer to the attached image for graph of g(x)
To determine the domain, we simply observe the x-axis.
The curve stretches through the x-axis, and there are no visible endpoints on the axis. This means that the curve starts from [tex]-\infty[/tex] to [tex]+\infty[/tex]
Hence, the domain of the function is: [tex](-\infty,\infty)[/tex]
To determine the range, we simply observe the y-axis.
The curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction. This means that the curve of g(x) is greater than 3 on the y-axis.
Hence, the range of the function is: [tex](3,\infty)[/tex]
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Function: [tex]g(x) = 3^{x} + 3[/tex]. Domain: [tex]Dom \{g(x)\} = \mathbb{R}[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex], respectively.
In Function Theory, the domain of a function [tex]f(x)[/tex] represents the set of values of the independent variable ([tex]x[/tex]), whereas the range of the function is the set of values of the dependent variable.
The Domain of the Function represents the set of values of [tex]x[/tex] (horizontal axis), whereas the Range it is the set of values of [tex]y[/tex] (vertical axis). After analyzing the existence of Asymptotes, we complement with graphic approaches and conclude where domain and range (in Interval notation) are.
Analytically speaking, the domain of exponential functions is the set of all real numbers and the range of [tex]g(x)[/tex] is any number between [tex]\lim_{x \to -\infty} g(x)[/tex] and [tex]\lim_{x \to +\infty} g(x)[/tex]. In a nutshell, we get the following conclusions in interval notation:
Domain: [tex]Dom \{g(x)\} = (-\infty, +\infty)[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex]
Lastly, we proceed to complement this analysis by graphing function with the help of a graphing tool.
According to the image, domain and range coincides with outcomes from analytical approaches.
Related Questions
Which of the following statements are true?
Answers
Answer:
last one
Step-by-step explanation:
they both whole
After a large fund drive to help the Boston City Library, the following information was obtained from a random sample of contributors to the library fund. Using a 1% level of significance, test the claim that the amount contributed to the library fund is independent of ethnic group.
Number of People Making Contribution
Ethnic Group $1-50 $51-100 $101-150 $151-200 Over $200 Row Total
A 77 63 54 39 18 251
B 90 48 76 26 24 264
C 73 67 59 37 30 266
D 108 82 70 50 30 340
Column Total 348 260 259 152 102 1121
Required:
a. What is the level of significance?
b. Find the value of the chi-square statistic for the sample.
c. Find or estimate the P-value of the sample test statistic.
d. Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
Answers
Answer:
α = 0.01 ; 2 - tailed
χ² = 16.998
Pvalue = 0.1497
Fail to reject H0
Step-by-step explanation:
Given the data above :
Number of People Making Contribution
Ethnic Group $1-50 $51-100 $101-150 $151-200 Over $200 Row Total
A 77 63 54 39 18 251
B 90 48 76 26 24 264
C 73 67 59 37 30 266
D 108 82 70 50 30 340
Column Total 348 260 259 152 102 1121
1.) The level of significance, α/2 = 0.01/2
2.)
The hypothesis :
H0 : Contribution and Ethnic group are independent
H1 : Contribution and Ethnic group are not independent
The Chisquare statistic :
χ² = (Observed - Expected)²/ Expected
The expected value for each cell is calculated thus :
(Row total * column total) / sum total
The expected values :
77.9197 58.2159 57.992 34.0339 22.8385
81.9554 61.231 60.9955 35.7966 24.0214
82.5763 61.6949 61.4576 36.0678 24.2034
105.549 78.8582 78.5549 46.1017 30.9367
Using the χ² formula above ;
χ² values for each cell are :
0.010855 0.393154 0.274794 0.724635 1.02509
0.789645 2.85902 3.69099 2.68108 0.0000191
1.11055 0.456179 0.098278 0.0240936 1.38826
0.056933 0.125176 0.93165 0.32963 0.028359
Taking the sum :
0.010855+0.393154+0.274794+0.724635+1.02509+0.789645+2.85902+3.69099+2.68108+0.0000191+1.11055+0.456179+0.098278+0.0240936+1.38826+0.056933+0.125176+0.93165+0.3293+0.028359
χ² = 16.998
To obtain the Pvalue :
df = (Row - 1)(column - 1) = (5-1)*(4-1) = 4 * 3 = 12
Pvalue(16.998 ; 12) = 0.1497
If Pvalue < α ; Reject H0 ;
Since Pvalue > α ; WE fail to reject H0
A ladder 10m long is set against a vertical wall, Calculate the height of the wall where the ladder reached a foot of the ladder is 6m away from the wall.
Answers
Answer:
8m
Step-by-step explanation:
The principal amount of money for this loan is $9,500.00. If you deposit this into an account paying 4.2% annual interest compounded monthly. How much money will be in the account after 5 years? (also called Future value).
Answers
9514 1404 393
Answer:
$11,715.65
Step-by-step explanation:
The applicable formula is ...
FV = P(1 +r/n)^(nt)
where principal P earns interest at rate r compounded n times per year for t years.
FV = $9500(1 +0.042/12)^(12·5) = $9500(1.0035^60) ≈ $11,715.65
The account will hold $11,715.65 after 5 years.
A spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 8?
Answers
Answer:
22/25
Step-by-step explanation:
Multiples of 8 are 8,16,24,32,40,48
That means there are 6 multiples of 8
50 -6 = 44
There are 44 non multiples of 8
P( non multiples of 8) = non multiples of 8 / total
= 44/50
=22/25
Two identical lines are graphed below. How many solutions are there to the system of equations?
A. Two
B. One
C. Zero
D. Infinitely many
Answers
Answer:
the answer is D. infinitely many
The number of solutions there are to the system of equations is Infinitely many, the correct option is D.
What is the Point-slope form?
The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
We are given that;
The two identical lines
Now,
We can find the equations of the two lines by using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
For line 1, we have two points (0,2) and (1,0), so we can find the slope as:
m1 = (0 - 2) / (1 - 0) = -2
Using point-slope form, we can write the equation of line 1 as:
y - 2 = -2(x - 0)
y = -2x + 2
For line 2, we have two points (-1,4) and (2,-2), so we can find the slope as:
m2 = (-2 - 4) / (2 - (-1)) = -2
Using point-slope form, we can write the equation of line 2 as:
y - 4 = -2(x - (-1))
y = -2x + 2
We can see that the two lines have the same slope and the same y-intercept.
Therefore, by the given slope of the line the answer will be infinitely many.
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Help for number 2a) b) c)
Thank you!! Make u the brainliest
Answers
9514 1404 393
Answer:
a) 300 square units
b) 260 square units
c) 264 square units
Step-by-step explanation:
The total surface area of a triangular prism is the sum of the areas of its 5 faces. Two of those are triangles (the bases), and three are rectangles. The area of an individual triangle is A = 1/2bh, but the area of the two of them together will be simply A = bh.
The area of the three rectangular faces is the sum of the products of the height of the prism and the edge length of each face. Then the sum of these products can be computed as the product of the height and the perimeter of the base.
These repetitive calculations are nicely done by a spreadsheet loaded with the appropriate formulas. Areas are all in "square units." (For problem 3, the units are centimeters.)
Example: (2a)
Base area = 5×12 = 60 . . . . combined area of both bases
Lateral area = (5 +12 +13)(8) = 30×8 = 240
Total surface area = 60 + 240 = 300 . . . . square units
Answer:
2. a. 300 units²
b. 260 units²
c. 264 units²
Step-by-step explanation:
2. a. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 12
h = 5
s1 = 13
s2 = 12
s3 = 5
H = 8
Plug in the values into the formula
Surface area of triangular prism = 12*5 + (13 + 12 + 5)*8
= 60 + (30)*8
= 60 + 240
Surface area = 300 units²
b. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 11
h = 3
s1 = 11
s2 = 5
s3 = 6.7
H = 10
Plug in the values into the formula
Surface area of triangular prism = 11*3 + (11 + 5 + 6.7)*10
= 33 + (22.7)*10
= 33 + 227
Surface area = 260 units²
c. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 6
h = 8
s1 = 10
s2 = 6
s3 = 8
H = 9
Plug in the values into the formula
Surface area of triangular prism = 6*8 + (10 + 6 + 8)*9
= 48 + (24)*9
= 48 + 216
Surface area = 264 units²
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Describe each data set, that is determine the shape, center, and spread
i. Sample mean for Car 1
ii. Sample mean for Car 2
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Ordered data:
Car 1 : 214, 220, 224, 239, 245, 295
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1437 / 6 = 239.5
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (224 + 239) /2 = 231.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 29.60 (using calculator)
Car 2 : 220, 221, 225, 244, 258, 259
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1427 / 6 = 237.833
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (225 + 244) /2 = 234.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 18.21 (using calculator)
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
b?
a=
b =
Answers
Answers:
a = 2
b = 3
=======================================================
Explanation:
Plug in x = 0 and y = 2 to find that
y = a*b^x
2 = a*b^0
2 = a*1
2 = a
a = 2
Then plug in x = 3 and y = 54 to determine the value of b
y = a*b^x
y = 2*b^x
54 = 2*b^3
2b^3 = 54
b^3 = 54/2
b^3 = 27
b = (27)^(1/3)
b = 3
So we have y = a*b^x update to y = 2*3^x
A bucket contains 4 red balls that are numbered 1, 2, 3, 4. It also contains 6 black balls that are numbered 5, 6, 7, 8, 9, 10. Two balls are drawn from the bucket, one at a time, without replacement. Use this information to answer the following probability questions. Express answers as fractions, or round decimal answers to 4 decimal places. a. What is the probability that the first ball is even and the second ball is odd
Answers
The probability is 1/9
We want to find the probability that the first drawn ball is even, and the second is odd.
The probability of randomly drawing an even ball will be equal to the quotient between the number of balls with even numbers and the total number of balls in the bucket.
We have a total of 10 balls (4 red ones and 6 black ones)
and 5 of these have even numbers (2, 4, 6, 8, 10)
Then the probability of drawing a ball with an even number first is:
p = 5/10 = 1/5
now we want to get a ball with an odd number.
notice that we already got a ball with an even number and we did not replace it, so now there are 9 balls left in the bucket, 5 odd ones, and 4 even ones.
The probability of getting an odd ball is computed in the same way thana above, as the quotient between the number of balls with odd numbers (5) and the total number of balls in the bucket (9)
q = 5/9
The joint probability (the probability that these two events happen together) is equal to the product of the individual probabilities, so we will get:
P = p*q = (5/9)*(1/5) = 1/9
The probability is 1/9
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find the sum of (-260)+(-30)
Answers
Answer:
-290
Step-by-step explanation:
(-260) +(-30)
=-260-30
=-290
Answer:
the answer is -290
Step-by-step explanation:
it is telling us to add so we can see that both the numbers have the same sign which is negative
when the signs are all the same, we can add and we got -290
so sánh 198*202 và 200^2
Answers
Step-by-step explanation:
198×202=39,996
200×200=40,000
hence,
39,9996 < 40,000
hope it helps
What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.
-5.8 ft
-6.3 ft
-27.5 ft
-69.1 ft
Answers
9514 1404 393
Answer:
69.1 ft
Step-by-step explanation:
The diameter of the circle is 24 ft. The length of the arc is more than twice the diameter, so cannot be less than about 50 ft. The only reasonable choice is ...
69.1 ft
__
The circumference of the circle is ...
C = 2πr = 2(3.14)(12 ft) = 75.36 ft
The arc length of interest is 330° of the 360° circle, so is 330/360 = 11/12 times the circumference.
s = (11/12)(75.36 ft) = 69.08 ft ≈ 69.1 ft
Answer:D
Step-by-step explanation:
25(0.3x-4)-5(1.5x-6)+100(13/4) simplify the following expression and evaluate for x=0.345
Answers
Answer:
255
Step-by-step explanation:
Given :
Simplify the expression :
25(0.3x-4)-5(1.5x-6)+100(13/4)
Open each Bracket:
7.5x - 100 - 7.5x + 30 + 325
7.5x - 7.5x - 100 + 30 + 325
= 255
The simplified equation = 255
Madison represented the sentence "The product of 3 and the difference of and the quotient of a number and is at most 5" by using the inequality . Which best describes Madison’s error?a) The difference of –4 and the quotient of a number and –2" should be written as . b) The product of 3 and the difference of –4 and the quotient of a number and –2" should be written as . c) The less than symbol should be replaced with the less than or equal to symbol. d) The less than symbol should be replaced with the greater than symbol.
Answers
Answer:
c) The less than symbol should be replaced with the less than or equal to symbol.
Step-by-step explanation:
3(-4 - n/-2) < 5
The equation written above could be interpreted as :
The product of 3 and the difference of -4 and the quotient of a number, n and -2 is less than 5
This means that the only error in Maddison's representation is the inequality sign, the inequality sign used by Maddison is wrong.
The equation should be used with a ≤ sign and expressed thus :
3(-4 - n/-2) ≤ 5
This means the left hand side (L. H. S) is less than or equal to 5 ; this means the L. H. S is at most 5
Answer:
C
Step-by-step explanation:
MY NOTES Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 2x2 − 4x + 3, [−1, 3
Answers
Answer:
b) [tex]c=1[/tex]
Step-by-step explanation:
From the question, we are told that:
Function
[tex]F(x)=2x^2-4x+9[/tex]
Given
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
Generally, the Function above is a polynomial that can be Differentiated and it is continuous
Where
-F(x) is continuous at (-1,3)
-F(x) Can be differentiated at (-1.3)
-And F(-1)=F(3)
Therefore
F(x) has Satisfied all the Requirements for Rolle's Theorem
Differentiating F(x) we have
[tex]F'(x)=4x-4[/tex]
Equating F(c) we have
[tex]F'(c)=0[/tex]
[tex]4(c)-4=0[/tex]
Therefore
[tex]c=1[/tex]
A particle is moving such that its height h at time t is given by h(t) = 2 + 8t - 3t^2 + 1/5t^3. The average velocity of the particle on the period [0,3] is
Answers
[tex]\\ \Large\sf\longmapsto h(t)[/tex]
[tex]\\ \Large\sf\longmapsto 2+8t-3t^2+\dfrac{1}{5}t^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+8(3)-3(3)^2+\dfrac{1}{5}(3)^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+24-3(9)+\dfrac{27}{5}[/tex]
[tex]\\ \Large\sf\longmapsto 26-27+5.4[/tex]
[tex]\\ \Large\sf\longmapsto -2+5.4[/tex]
[tex]\\ \Large\sf\longmapsto h(t)=3.4m[/tex]
is jannelle correct ?
Answers
Answer:
yes
Step-by-step explanation:
o
Find the length represented by x for each pair of similar triangles.
18cm, 9cm, and x
30cm, 15cm, and 25cm
Answers
Answer:
15 cm
Step-by-step explanation:
Since the traingles are similar, we can find the ratio between the side lengths, and it will be the same for each side.
We can use the side length 9 and 15 to find this ratio. 15/9=5/3. So, the ratio of a side length of the larger triangle to the smaller one is 5/3, so our equation becomes 5/3 = 25/x. Use any method you like to find that x=15.
Hope this helped,
~cloud
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.
Step 1 of 2: Suppose a sample of 2845 tenth graders is drawn. Of the students sampled, 2276 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Step 2 of 2: Suppose a sample of 2845 tenth graders is drawn. Of the students sampled, 2276 read above the eighth grade level. Using the data, construct the 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
Answers
Answer:
Step 1: The estimate the proportion of tenth graders reading at or below the eighth grade level is 0.2.
Step 2: The 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.181, 0.219).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose a sample of 2845 tenth graders is drawn. Of the students sampled, 2276 read above the eighth grade level.
So 2845 - 2276 = 569 read below, and the estimate of the proportion of tenth graders reading at or below the eighth grade level is:
[tex]\pi = \frac{569}{2845} = 0.2[/tex], and the answer to step 1 is 0.2.
The sample size is [tex]n = 2845[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 2.575\sqrt{\frac{0.2*0.8}{2845}} = 0.181[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 2.575\sqrt{\frac{0.2*0.8}{2845}} = 0.219[/tex]
The 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.181, 0.219).
The price of a item has reduced by 85% the original price was $60
Answers
Answer:
The price now would be 9 dollars
Step-by-step explanation:
60 x 85% is 51 and you subtract that from 60
which of the following statements is true? -6 < -8 -6> -8 or -6=-8
Answers
Answer:
-6>-8
Step-by-step explanation:
-6 is more than -8.
Determine the measure of the interior angle at vertex E.
A. 50
B. 90
C. 30
D. 150
PLS REPLY FAST THIS IS URGENT
Answers
B. 90
Step-by-step explanation:
4x + 4x + 3x + 3x + 4x = 540
x = 30
Vertex E = 3x where x = 30
3x = ?
3(30) = 90
Vertex E = 90*
The measure of the interior angle at vertex E can be determined by using the properties of triangles. In a triangle, the sum of all interior angles is always 180 degrees.
Therefore, to find the measure of the interior angle at vertex E, we need to subtract the measures of the other two angles at vertices A and B from 180 degrees. Let's assume that the measures of the angles at vertices A and B are a and b degrees, respectively. Then, the measure of the interior angle at vertex E can be calculated as follows: Interior angle at vertex E = 180 degrees - (measure of angle at vertex A + measure of angle at vertex B) Now, let's refer back to the given answer choices: A. 50 B. 90 C. 30 D. 150 Without additional information or a diagram, it is not possible to determine the exact measures of the angles at vertices A and B. Therefore, we cannot directly calculate the measure of the interior angle at vertex E. In order to solve this problem, we need more information about the triangle or a diagram that shows the relative positions of the vertices.
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The value of f(x)= 5x -4x²+3 when x= -1, is
Answers
Answer:
F(x) =5(-1)-4(-1)^2+3,
=-5-4+3
=-6
Which graph represents the function f(x) = x-2?
Answers
Answer:
click in photo
nejdjjd
nxndjdbbdjf
lấy x=0 ta có y= -2 => A(0;-2)
lấy y=0 ta có x=2 => B(2;0)
nối 2 điểm A và B ta có đồ thị:
Cho hình hộp chữ nhật ABCD A B C D
Answers
Answer:
A B C D
A×B×C×D
3×3×3×6
162
Family Video stocks 1003 drama movies, 518 science fiction movies and
253 children's movies. How many more drama titles than children's
titles does Family Video have in stock?
Answers
Answer:
There are 750 more drama movies that children's movies.
Step-by-step explanation:
There are 1003 drama movies, and 253 children's movies.
1003 - 253 = 750
Charlotte has to read a book for school. There are 513 pages in the book. She read 113 pages on
Saturday, she read 78 pages on Sunday, and 101 pages on Monday. How many pages does Charlotte
have left to read?
A.221 pages
B.513 pages
C.292 pages
D.400 pages
Answers
represent (-12)+(-8)+14 on a number line
Answers
Answer:
-6
Step-by-step explanation:
(-12)+(-8)= -20
-20+14= -6
Which of the following rational functions is graphed below?
o
A. F(x) = 1/2x
B. AX) = 1/x-2
C. F(x) = 1/x+2
Answers
Answer:
Option B.
Step-by-step explanation:
We can see that we have an asymptote at x = 2
Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.
So, the denominator is something like:
(x + a)
we have that the denominator is zero when x = 2
Then:
(2 + a) = 0
solving that for a, we get:
a = -2
Then the denominator of the rational function is:
(x - 2)
For the given options, the only one with this denominator is option B, then the correct option is B.
Answer:
B. f(x) = 1/x-2
Step-by-step explanation:
Math is ez bro.
