Quiz about Square Root & Quadratic Inverses

Question 1

Find the inverse function of $$f\left(x\right)=\sqrt{x}-6$$

Accepted Answer

$$f^{-1}\left(x\right)=\left(x+6\right)^2$$

Answer

$$f^{-1}\left(x\right)=\left(x-6\right)^2$$

Answer

$$f^{-1}\left(x\right)=x^2+6$$

Answer

$$f^{-1}\left(x\right)=x^2+36$$

Question 2

Find the inverse function of $$y=\left(x-4\right)^2+3$$

Accepted Answer

$$y=\sqrt{x-3}+4$$

Answer

$$y=\sqrt{x+3}-4$$

Answer

$$y=\sqrt{x-3+4}$$

Answer

$$y=\sqrt{3x+1}$$

Question 3

Find the inverse function of $$y=-6+\left(x+10\right)^2$$

Accepted Answer

$$y=\sqrt{x+6}-10$$

Answer

$$y=\sqrt{x-6}+10$$

Answer

$$y=\sqrt{x-10}+6$$

Answer

$$y=\sqrt{x+10}-6$$

Question 4

Find the inverse function of $$y=-2+\sqrt{x+7}$$

Accepted Answer

$$y=\left(x+2\right)^2-7$$

Answer

$$y=\left(x-2\right)^2+7$$

Answer

$$y=\left(x+7\right)^2-2$$

Answer

$$y=\left(x-7\right)^2+2$$

Question 5

What does it mean to find the inverse of a function?

Accepted Answer

the x's and y's are switched

Answer

the x's and y's are divided by 2

Answer

the x's and y's are made negative

Answer

the x's and y's are the same

Question 6

Are the relations inverses?

Accepted Answer

no

Answer

yes

Question 7

Find the inverse of the quadratic function: $$f\left(x\right)=\left(x-6\right)^2+3$$

Accepted Answer

$$f^{-1}\left(x\right)=\sqrt[]{x-3}+6$$

Answer

$$f^{-1}\left(x\right)=\sqrt[]{x-6}+3$$

Answer

$$f^{-1}\left(x\right)=\sqrt[]{x+3}-6$$

Answer

$$f^{-1}\left(x\right)=\sqrt[]{x+6}-3$$

Question 8

Which is the inverse of the table?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 9

Are the blue and red graphs inverse functions?

Accepted Answer

Kind of... the graphs reflect over y = x; however the quadratic is invertible without restriction on the domain.

Answer

No, they do not reflect over the line y = x.

Answer

Yes, the functions reflect over the line y = x.

Question 10

Find the inverse of $$f\left(x\right)=\sqrt{x+2}+9$$

Accepted Answer

$$f\left(x\right)=\left(x-9\right)^2-2$$

Answer

$$f\left(x\right)=\left(x+9\right)^2+2$$

Answer

$$f\left(x\right)=\sqrt{x+9}+2$$

Answer

$$f\left(x\right)=\sqrt{x-9}-2$$

Question 11

What does it mean to find the inverse of a function?

Accepted Answer

the x's and y's are switched

Answer

the x's and y's are divided by 2

Answer

the x's and y's are made negative

Answer

the x's and y's are the same

Question 12

The inverse has been reflected over which line?

Accepted Answer

y = x

Answer

y =1

Answer

y = 0

Answer

y = x + 1

Question 13

Find the INVERSE equation

$$y=\left(x+1\right)^2$$

Accepted Answer

$$f^{-1}\left(x\right)=\pm\ \sqrt{\ x}-1$$

Answer

$$f^{-1}\left(x\right)=\pm\ \sqrt{x-1\ }$$

Answer

$$f^{-1}\left(x\right)=\pm\ \sqrt{\ x}+1$$

Answer

$$f^{-1}\left(x\right)=\pm\ \left(x-1\right)^2$$

Question 14

After swapping x & y, what is the FIRST STEP when finding the inverse of the equation

$$y=\left(x+5\right)^2-3$$

Accepted Answer

Add 3 to both sides.

Answer

Subtract 5 from both sides

Answer

Square root both sides

Answer

Add 5 to both sides.

Question 15

Identify the inverse function

$$y=\sqrt{\ x+5}-1$$

Accepted Answer

$$f^{-1}\left(x\right)=\left(x+1\right)^2-5$$

Answer

$$f^{-1}\left(x\right)=-\left(x-5\right)^2+1$$

Answer

$$f^{-1}\left(x\right)=\left(x-1\right)^2+5$$

Answer

$$f^{-1}\left(x\right)=\left(x+4\right)^2$$

Question 16

The domain of a square root function is $$\left[4,\infty\right)$$ .

What is the RANGE of the inverse?

Accepted Answer

$$\left[4,\infty\right)$$

Answer

$$\left[-4,\infty\right)$$

Answer

$$\left(-\infty\ ,4\right]$$

Answer

$$\left[-4,\infty\right)$$

Question 17

Identify the inverse function.

$$y=\left(x-2\right)^2$$

Accepted Answer

$$y=\pm\ \sqrt{\ x}+2$$

Answer

$$y=\pm\ \sqrt{\ x}-2$$

Answer

$$y=\pm\ \sqrt{\ x+2}$$

Answer

$$y=\pm\ \sqrt{\ x-2}$$

Question 18

The RED function is a square root.

Is the BLUE function the inverse?

Accepted Answer

Yes, they are inverses.

Answer

No, they are NOT inverses.

Answer

Not enough information.

Question 19

The BLUE function is the original.

Is the GREEN function the inverse?

Accepted Answer

The blue function is not invertible, but if you restrict the domain, then they could be inverses.

Answer

No, they are NOT inverses.

Answer

Yes, they are inverses.

Question 20

The BLUE function is the original.

Is the PURPLE function the inverse?

Accepted Answer

No, they are NOT inverses.

Answer

Yes, they are inverses.

Answer

There is not enough information.

Question 21

If $$f\left(x\right)=\left(x+6\right)^2,\ x\ge-6$$ , find $$f^{-1}\left(x\right)$$ and restrict the domain if necessary.

Accepted Answer

$$f^{-1}\left(x\right)=\sqrt[]{x}-6$$

Answer

$$f^{-1}\left(x\right)=\sqrt[]{x+6}$$

Answer

$$f^{-1}\left(x\right)=-\ \sqrt[]{x}-6$$

Answer

$$f^{-1}\left(x\right)=-\ \sqrt[]{x+6}$$

Question 22

If $$f\left(x\right)=\sqrt[]{x+5}-3$$ , find $$f^{-1}\left(x\right)$$ and restrict the domain if necessary.

Accepted Answer

$$f^{-1}\left(x\right)=\left(x+3\right)^2-5,\ x\ge-3$$

Answer

$$f^{-1}\left(x\right)=\left(x+3\right)^2-5,\ x\le-3$$

Answer

$$f^{-1}\left(x\right)=\left(x-5\right)^2+3,\ x\ge5$$

Answer

$$f^{-1}\left(x\right)=\left(x-5\right)^2+3,\ x\le5$$

Question 23

If $$f\left(x\right)=x^2+9,\ x\le0$$ , find $$f^{-1}\left(x\right)$$ and restrict the domain if necessary.

Accepted Answer

$$f^{-1}\left(x\right)=-\ \sqrt[]{x-9}$$

Answer

$$f^{-1}\left(x\right)=\sqrt[]{x-9}$$

Answer

$$f^{-1}\left(x\right)=\sqrt[]{x}+9$$

Answer

$$f^{-1}\left(x\right)=-\ \sqrt[]{x}+9$$

Question 24

If $$f\left(x\right)=\sqrt[]{5x}$$ , find $$f^{-1}\left(x\right)$$ and restrict the domain if necessary.

Accepted Answer

$$f^{-1}\left(x\right)=\frac{1}{5}x^2,\ x\ge0$$

Answer

$$f^{-1}\left(x\right)=\frac{1}{5}x^2,\ x\le0$$

Answer

$$f^{-1}\left(x\right)=x^2-5,\ x\ge0$$

Answer

$$f^{-1}\left(x\right)=x^2-5,\ x\le0$$

Question 25

If $$f\left(x\right)=x^2+2,\ x\ge0$$ , find $$f^{-1}\left(x\right)$$ and restrict the domain if necessary.

Accepted Answer

$$f^{-1}\left(x\right)=\sqrt[]{x-2}$$

Answer

$$f^{-1}\left(x\right)=-\ \sqrt[]{x-2}$$

Answer

$$f^{-1}\left(x\right)=\sqrt[]{x}+2$$

Answer

$$f^{-1}\left(x\right)=-\ \sqrt[]{x}+2$$

Question 26

If $$f\left(x\right)=\sqrt[]{x-5}+2$$ , find $$f^{-1}\left(x\right)$$ and restrict the domain if necessary.

Accepted Answer

$$f^{-1}\left(x\right)=\left(x-2\right)^2+5,\ x\ge2$$

Answer

$$f^{-1}\left(x\right)=\left(x-2\right)^2+5,\ x\le2$$

Answer

$$f^{-1}\left(x\right)=\left(x+5\right)^2-2,\ x\ge-5$$

Answer

$$f^{-1}\left(x\right)=\left(x+5\right)^2-2,\ x\le-5$$

Question 27

Determine the inverse for Example C in your notes:

$$f\left(x\right)=\sqrt[]{x-3}-7$$

Accepted Answer

P^-1(x) = $$\left(x+7\right)^2+3$$

Answer

P^-1(x) = $$\frac{\left(x^2-3\right)}{7}$$

Answer

P^-1(x) = $$\left(x+7\right)^2-3$$

Answer

P^-1(x) = $$\sqrt[]{\frac{x-7}{3}}$$

Question 28

Generate the inverse of the function represented in the table.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Question 29

The graph of the function

$$f\left(x\right)=\left(x-2\right)^3-5$$ is shown.

If the point (4, 3) is on the graph of f(x), give the point on the graph of the inverse that corresponds.

Accepted Answer

(3, 4)

Answer

(-4, -3)

Answer

(-3, -4)

Answer

no point would correspond

Question 30

The inverse of the function f(x) is written as ...

Accepted Answer

f -1(x)

Answer

f 2(x)

Answer

f '(x)

Answer

f +(x)

Question 31

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

Accepted Answer

(2, 1) (8, 3) (6, -3)

Answer

(1, 2) (3, 8) (-3, 6)

Answer

(1, 2) (8, 3) (-3, 6)

Answer

(-1, -2) (-3, -8) (3, -6)

Question 32

What does it mean to find the inverse of a function?

Accepted Answer

the x's and y's are switched

Answer

the x's and y's are divided by 2

Answer

the x's and y's are made negative

Answer

the x's and y's are the same

Question 33

Which is the inverse of the table?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 34

Find the inverse function of $$y=\sqrt{x+11}$$

Accepted Answer

$$y=x^2-11$$

Answer

$$y=x^2+11$$

Answer

$$y=\left(x+11\right)^2$$

Answer

$$y=\left(x-11\right)^2$$

Question 35

Find the inverse function of $$f\left(x\right)=\sqrt{x}-6$$

Accepted Answer

$$y=\left(x+6\right)^2$$

Answer

$$y=\left(x-6\right)^2$$

Answer

$$y=x^2+6$$

Answer

$$y=x^2+36$$

Question 36

Find the inverse of $$f\left(x\right)=\sqrt{x+2}+9$$

Accepted Answer

$$f\left(x\right)=\left(x-9\right)^2-2$$

Answer

$$f\left(x\right)=\left(x+9\right)^2+2$$

Answer

$$f\left(x\right)=\sqrt{x+9}+2$$

Answer

$$f\left(x\right)=\sqrt{x-9}-2$$

Question 37

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

Accepted Answer

solve for y

Answer

replace y with f^-1(x)

Answer

solve for x

Answer

find the greatest common factor

Question 38

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

Accepted Answer

(4, 1) and (6, 4)

Answer

(1, 4) and (4, 6)

Answer

(-4, -1) and (-6, -4)

Answer

(-1, -4) and (-4, -6)

Question 39

What is the best description?

Accepted Answer

They are inverse functions.

Answer

They are both functions, but not inverse functions.

Answer

They are reflected over y=x, but they are not both functions.

Answer

They are not reflected over y=x, and they are not both functions.

Question 40

The domain of a square root function is $$\left[4,\infty\right)$$ .

What is the RANGE of the inverse?

Accepted Answer

$$\left[4,\infty\right)$$

Answer

$$\left[-4,\infty\right)$$

Answer

$$\left(-\infty\ ,4\right]$$

Answer

Cannot be determined

Question 41

The inverse has been reflected over which line?

Accepted Answer

y = x

Answer

y =1

Answer

y = 0

Answer

y = x + 1

Question 42

Domain is:

Accepted Answer

All x values, from left to right.

Answer

All y values, from bottom to top.

Answer

All x values from bottom to top.

Answer

All y values from left to right.

Question 43

Range is:

Accepted Answer

All y values, from bottom to top.

Answer

All x values, from left to right.

Answer

All x values from bottom to top.

Answer

All y values from left to right.

Question 44

What is the y-intercept of the graph?

Accepted Answer

(0,3)

Answer

(-1,0)

Answer

(0,-1)

Answer

(3,0)

Question 45

The inverse of the function f(x) is written as ...

Accepted Answer

f -1(x)

Answer

f 2(x)

Answer

f '(x)

Answer

f +(x)

Question 46

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

Accepted Answer

(2, 1) (8, 3) (6, -3)

Answer

(1, 2) (3, 8) (-3, 6)

Answer

(1, 2) (8, 3) (-3, 6)

Answer

(-1, -2) (-3, -8) (3, -6)

Square Root & Quadratic Inverses

55 questions

What does it mean to find the inverse of a function?

Are the relations inverses?

Which is the inverse of the table?

Are the blue and red graphs inverse functions?

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