How does a domain restriction placed on a non-invertible function affect its inverse? Drag a function or an interval into each box to correctly complete the statement. When the domain of the non-invertible function f(x)=(x+1)^2−3 is [−1,∞), the inverse of the function is Response area, and the domain of the inverse function is

Answers

Answer 1

Using inverse function concepts, it is found that:

The inverse of the function is [tex]y = \sqrt{x + 3} - 1[/tex], and the domain of the inverse function is [tex][-3, \infty][/tex].

A function will have an inverse if for each output, there is only one respective input.The domain of the inverse is the range of the original function.

The function given is:

[tex]f(x) = (x + 1)^2 - 3[/tex]

It's range is [tex][-3, \infty][/tex], which will be the domain of the inverse.

To find the inverse, we exchange x and y, and isolate y, then:

[tex]y = (x + 1)^2 - 3[/tex]

[tex]x = (y + 1)^2 - 3[/tex]

[tex](y + 1)^2 = x + 3[/tex]

[tex]\sqrt{(y + 1)^2} = \sqrt{x + 3}[/tex]

[tex]y + 1 = \sqrt{x + 3}[/tex]

[tex]y = \sqrt{x + 3} - 1[/tex]

The inverse of the function is [tex]y = \sqrt{x + 3} - 1[/tex], and the domain of the inverse function is [tex][-3, \infty][/tex].

A similar problem is given at https://brainly.com/question/13160937

Answer 2

Answer:

Step-by-step explanation:

How Does A Domain Restriction Placed On A Non-invertible Function Affect Its Inverse? Drag A Function

Related Questions

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function . How long does it take for the baseball to reach its maximum​ height? What is the​ baseball?s maximum​ height?

Answers

Answer:

Step-by-step explanation:

Let the initial velocity of the ball is u.

At the maximum height the speed is zero.

Let the time is t.

Use first equation of motion.

v = u - gt

0 = u - g t

t = u/g

Let the maximum height is H.

Use third equation of motion

[tex]v^2 = u^2 - 2 gh\\\\0 = u^2 - 2 gH\\\\H = \frac{u^2}{2 g}[/tex]

Pls what is the formula for finding the base and the height of a triangular pyramid.

Answers

Answer:

Take the Cubits and multiply

Step-by-step explanation:

This is a problem i had so just fill it in to your numbers etc.

A= 43.3 cubits squared

SA= the base of A +1/2 (p x slant h)

SA= 43.3 cubits squared + 1/2 (30 x 14 cubits)

To sum it up u can message me ur numbers and ill help

The following formula gives the area A of a trapezoid, where b and c are the bases of the trapezoid and h
is the height:
A=
(6+c)h
Rearrange the formula to highlight the height.
h

Answers

Answer:

[tex]h = \frac{2A}{b + c}[/tex]

Step-by-step explanation:

Given

[tex]A = \frac{1}{2}(b + c)h[/tex]

Required

Solve for h

We have:

[tex]A = \frac{1}{2}(b + c)h[/tex]

Multiply sides by 2

[tex]2A = (b + c)h[/tex]

Make h the subject

[tex]h = \frac{2A}{b + c}[/tex]

Place parentheses in the following equation to make it true.
6+6/6x6-6= 0

Answers

Answer: (6+6/6)*(6-6)= 0

help mee pls plss fast

Answers

Difference between a 1 inch button and ⅜ inch button

[tex] = 1 \: inch - \frac{3}{8} \: inch \\ = \frac{8}{8} \: inch - \frac{3}{3} \: inch \\ = \frac{(8 - 3)}{8} \: inch \\ = \frac{5}{8} \: inch[/tex]

Answer:

5/8

Step-by-step explanation:

To determine the difference, we do:

1 - 3/8

8/8 - 3/8

5/8

A 1 inch button is 5/8 inches longer than a 3/8 inch button.

Complete the equation to represent finding x, the greater integer. x(x – ) = 143 What is the greater integer?

Answers

Answer:

[tex]x * (x - 2) = 143[/tex]

Where [tex]x = 13[/tex]

Step-by-step explanation:

Given

[tex]x (x - \_) = 143[/tex]

Required

Complete the blank

The complete question implies that the product include 2 consecutive odd numbers.

Two numbers whose products equal 143 are: 11 and 13

i.e. [tex]11 * 13 = 143[/tex]

So, we have:

[tex]x * (x - \_) = 13 * 11[/tex]

By comparison, we have:

[tex]x = 13[/tex]

[tex]x - \_ = 11[/tex]

Collect like terms

[tex]\_ = x - 11[/tex]

Substitute 13 for x

[tex]\_ = 13 - 11[/tex]

[tex]\_ = 2[/tex]

So, the complete equation is:

[tex]x * (x - 2) = 143[/tex]

Where [tex]x = 13[/tex]

Answer:

2

and

13

Step-by-step explanation:

Got it right on edge.

(a) Tom says that 1/5 + 7/20 = 8/25
Explain why he is wrong and show how to work out the correct answer.
(b) Show that 3/4 divided by 1 7/8 = 2/5
9. (a) Jadar is buying fencing to fence one side of his garden. He measures the length as 23cm to the nearest metre.
What is the largest possible true length of the garden?
(b) One post measures 180 cm truncated to 2 significant figures (Truncated means that rather than rounding, any digits after 2 significant figures are simply ignored

Answers

numerator = top part of the fraction

denominator = bottom part of the fraction

* means multiply

a.

you can only add the numerator when the denominator is the same

cant add the denominator

denominator has to be the same

1/5 = 4/20

4/20 + 7/20 = 11/20

b.

1 7/8 = 15/8

3/4 ÷ 15/8 =

3/4 * 8/15 =

24/60 = divide both top and bottom by 12 =

2/5

Step-by-step explanation:

a)1/5+ 7/20

1.find the CM of both denominators

2.multiply both the denominator and the numerator using the CM

=(1/5)×20 +(7/20)

=20/100 +35/100

since you multiply

3.Now add both numerators ( don't add the denominators)

=the answer is 55/100

Which are the solutions of x2 = –13x – 4?

Answers

Answer:

The 3rd dot and 4th dot, you should select to get the correct answer.

Joe has four notes in his wallet. The total value of the notes is $75. Which type of note is not in Joe's wallet?

Answers

Answer:

$ 20

Step-by-step explanation:

Given that,

No. of notes Joe has = 4

The total value of the notes = $ 75

From the given notes, 4 notes that can make the sum of 75 would be

$ 50 note + $ 10 + $ 10 note + $ 5

= 50 * 1 + 10 * 1 + 10 * 1 + 5 * 1

= $ 75  

Thus, the note that would not be included in the total value would $20 note as if we add it either the sum would be greater or lesser with four notes in combination.

Find the value of b. PLEASE HELP ASAPPPP!!!!
A. 56
B. 140
C. 230
D. 65

Answers

Answer:

C

Step-by-step explanation:

b=360-2(65)=360-130=230

Answer:

230

Step-by-step explanation:

b= 360-2(65)

=360-130

=230

Use the special angles to evaluate: a) cosec 60° cot 30° + cos 45º cosec 45° 2​

Answers

Answer:

the required answer is 4√2+1/2√2

Please hurry I will mark you brainliest

Answers

Step-by-step explanation:

I think you first have to calculate a°,this can be done by first finding c°

c°=180-125

=55°

opposite angles in a quadrilateral add up to 180

therefore a°=180-55

=125

therefore angle d

180-125

=55

I hope this helps

A graph is shown.
How do you determine if this is a function or not? Is this a function. Help please

Answers

Answer:

Not a function

Step-by-step explanation:

we see on this graph,

(1,2) and (1,7)

we have two of the same x points, when put on a graph, that would be having 2 of the same inputs.

which always means it's not a function.

Please help me: -3/4(8h + 12) = 3(n - 3)

Answers

Answer:

n = 0

Step-by-step explanation:

[tex]-\frac{3}{4}(8n+12)=3(n-3)\\\\-6n-9=3n-9\\\\-9n-9=-9\\\\-9n=0\\\\ n=0[/tex]

Answer:

n = 0

Step-by-step explanation:

-3/4(8h + 12) = 3(n - 3)

-6h - 9 = 3n - 9

-6h - 3n = -9 + 9

-9n = 0

n = 0

Rewrite the expression with rational exponents as a radical expression.

4 times x to the three sevenths power

Answers

Answer:

[tex]\displaystyle 4\sqrt[7]{x^3}[/tex]

General Formulas and Concepts:

Algebra I

Exponential Rule [Root Rewrite]:                                                                        [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle 4x^\bigg{\frac{3}{7}}[/tex]

Step 2: Rewrite

Split:                                                                                                                      [tex]\displaystyle 4(x^\bigg{\frac{1}{7}})^3[/tex]Rewrite [Exponential Rule - Root Rewrite]:                                                        [tex]\displaystyle 4\sqrt[7]{x^3}[/tex]

Jeff and his friends win a prize.
Jeff's share is $160 which is ĭ of the prize.
Work out the value of the prize.

Answers

Answer:

Prize, P = $352

Step-by-step explanation:

Let Jeff's share be J.Let the value of the prize be P.

Given the following data;

J = $160J = 5P/11

To find the value of the prize;

[tex] \frac {5}{11} * P = 160 [/tex]

[tex] \frac {5P}{11} = 160 [/tex]

Cross-multiplying, we have;

[tex] 5P = 160 * 11 [/tex]

[tex] 5P = 1760 [/tex]

[tex] P = \frac {1760}{5} [/tex]

Prize, P = $352

Find the measures of the indicated angle

Answers

Answer:

76

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin ? = 32/33

Taking the inverse sin of each side

sin ^-1( sin ?) = sin^-1 (32/33)

? =75.85888

To the nearest degree

? = 76

On a map, 1 in represents 420 miles. How much does 3/4 in represent?

Answers

Answer:

315

Step-by-step explanation:

420 x 3/4 = 315

Answer:

315 miles

Step-by-step explanation:

We can write a ratio to solve

1 inch          3/4 inches

------------   = ---------------

420 miles     x miles

Using cross products

1 * x = 420 * 3/4

x=315

The lengths of two sides of a triangle are 11 cm and 19 cm. Identify the range of possible lengths for the third side.

Answers

Answer:

2nd option

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

19 - 11 < x < 19 + 11

8 < x < 30

Answer:

8 < x < 30

Step-by-step explanation:

The rule for side lengths of a triangle is:

the sum of two side's must be bigger than the third side and their difference must be smaller than the third side :

19 - 11 < x < 19 + 11

8 < x < 30

Determine the sum of the first 19 terms of the following series:

6−12+24−48+

Answers

Answer:

6-12

24-48

6-2424-196dirst 6 multiplied by four same next series

Which is the equation of the line with y-intercept -2 and slope 6.

Answers

Answer:

The equation would be y=m-2+6

Step-by-step explanation:

Have a great day :)

PLEASE ANSWER ASAP

Write an inequality and show on a number line all numbers: greater than (-3) but less than or equal to 3

Answers

Answer:

The inequality is -3<x<3

Step-by-step explanation:

(-3,3)

What is the value of x in the diagram below?
X + 2
8.
х

Answers

Answer:

15

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +8^2=(x+2)^2[/tex]

we can simplify 8 squared to 64, and we can use FOIL to expand x plus 2 squared.

[tex](x+2)(x+2)=x^2+4x+4[/tex]

We have

[tex]x^2+64=x^2+4x+4[/tex]

We can subtract x squared plus four from both sides to get

[tex]60=4x[/tex]

Dividing by 4, we get [tex]x=15[/tex]

Answer:x=15

Step-by-step explanation:

remember the Pythagorean Theraum(sorry about spelling)

a^2 +b^2=c^2

the shortest is a^2 , b^2 is the second shortest, and c^2 is the hypotenuse, or the longest.

currently the hypotenuse (c^2)is x+2, (b^2) is x, and a^2 is 8

8x8=64

64+x^2=(x+2)^2

try solving it now.

64+15^2=(15+2)^2

289=289

So, x=15

Analyze the problem and complete the statements.
t-7 = 8
I know this problem is an
because it has an equals sign.
The t is the
The negative sign is the
The 7 and the 8 are both

Answers

Answer:

I know this problem is an  

✔ equation

because it has an equals sign.

The t is the  

✔ variable

.

The negative sign is the  

✔ operation

.

The 7 and the 8 are both  

✔ constants

.

Step-by-step explanation: i took the test :( crying cuz im bouta fail

(0.053) (0.578)
Multiply the numbers

Answers

Answer:

If you multiply the numbers you will get

0.030634

Please help me i will give brainliest!

Answers

Answer:

10

Step-by-step explanation:

1x2x2.5=5

5/0.5=10

Answer:

= 40 cubes

Step-by-step explanation:

volume = 2.5×2×1 = 5cm^2

volume of cubes = 0.5×0.5×0.5 = 0.125cm^2

5÷0.125 = 40

= 40 cubes

Evaluate f(x) when x = 3.

Answers

Answer:

56

Step-by-step explanation:

Since 3 is between -6 and 9 we use the first definition

f(3) = 6 x^2 +2

     = 6(3)^2+2

    = 6(9) +2

   = 54+2

    = 56

The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports to test the claim that they are from a population having a mean less than 6.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses?


T-Test


μ<4.00


t=-3.033077


p=0.002025


x=3.48


Sx=1.150075


n=45

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the T test output :

T-Test

μ<4.00

t=-3.033077

p=0.002025

x=3.48

Sx=1.150075

n=45

Given that population mean, μ = 6

Confidence level, α = 0.05

The hypothesis :

H0 : μ = 6.00

H1 : μ < 6.00

From the t test output given :

The test statistic :

T = -3.033077

T = - 3.03 (2 decimal places)

The Pvalue :

P = 0.002025

Pvalue = 0.002 (3 decimal places)

The conclusion :

Decision region ; Reject H0 : if Pvalue < α

Since ; Pvalue < α

Reject H0 ; There is sufficient evidence to support claim that sample is from a population with a mean less than 6.

Which is an equivalent equation solved for g? StartFraction A t Over 60 EndFraction equals g.= g StartFraction A Over 60 t EndFraction equals g. = g StartFraction 60 A Over t EndFraction equals g. = g 60At = g

Answers

Answer:

A. StartFraction A t Over 60 EndFraction equals g

g = At/60

Step-by-step explanation:

The goals against average (A) for a professional hockey goalie is determined using the formula A = 60 a equals 60 left-parenthesis StartFraction g Over t EndFraction right-parenthesis.. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes. Which is an equivalent equation solved for g?

A. StartFraction A t Over 60 EndFraction equals g

B. StartFraction A Over 60 t EndFraction equals g

C. StartFraction 60 A Over t EndFraction equals g. = g 60At = g

Given equation:

A = 60(g/t)

Where,

A = Average goal

g = number of goals scored against the goalie

t = the time played

Which is an equivalent equation solved for g?

A = 60(g/t)

Open parenthesis

A = 60g / t

Cross product

A * t = 60g

At = 60g

Divide both sides by 60

g = At/60

Answer:

At/60 = g

( option A )

\He wants to buy at least 5 goats. Write down an inequality in x to represent this

Answers

Answer:

x≥5

Step-by-step explanation:

If x is the quantity of goats he wants x≥5

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