Free Printable 2.8 - Inverse Functions

1.

What are the inverse points for the coordinates:

(3, 0) , (2, -4), (5, 5) and (-6,8)

a)

(3,0) , (2, -4) , (5,5) , (6,8)

b)

(0,3) , (-4,2) , (5,5) , (8,-6)

c)

(3,2), (0, -4), (5, -6), (5,8)

2.

Are these inverse functions?

a)

yes

b)

no

3.

Are these functions inverses?

a)

No

b)

Yes

c)

No way to tell

4.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

5.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

d)

6.

Find the inverse of $f(x)=10+7x$

a)

$f^{-1}(x)=\frac{x-7}{10}$

b)

$f^{-1}(x)=\frac{x-10}{7}$

c)

$f^{-1}(x)=\frac{1}{10+7x}$

7.

Find the inverse of $f(x)=\frac{x-5}{3}$

a)

$f^{-1}(x)=\frac{3}{5}+x$

b)

$f^{-1}(x)=3x+5$

c)

$f^{-1}(x)=5x+3$

8.

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

a)

the x's and y's are switched

b)

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

c)

the x's and y's are made negative

d)

the x's and y's are the same

9.

Find the correct order to find the inverse of f(x)= 2x-5

a)

y=2x-5

b)

2y-5=x

c)

2y= x+5

d)

$y=\frac{x+5}{2}$

e)

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

1)

2)

3)

4)

5)

10.

Find the inverse of $f\left(x\right)=\frac{1}{4}x-7$

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x+28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x+28

11.

The graph of the function y=g(x) is shown below. The value of

g^{-1}\left(2\right)

is

a)

2.5

b)

-4

c)

0.4

d)

-1

12.

Which of the following functions would have an inverse that is also a function?

a)

b)

c)

d)

13.

If the domain of y=h(x) is [-5,4] and its range is [-4,1], what is the domain of $y=h^{-1}\left(x\right)$ ?

a)

[4,-5]

b)

[5,-4]

c)

[-4,1]

d)

[4,-1]

14.

Find the inverse of $f\left(x\right)=x^2+5$ with domain $x\ge0$

a)

$f^{-1}\left(x\right)=x-25$

b)

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

c)

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

d)

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

15.

are these inverse functions?

a)

no

b)

yes

c)

no way to tell

16.

f(x) = {(3, 7), (4, -2), (5, -1), (8, 7)}
Is f^-1(x) a function?

a)

Yes

b)

No

c)

No way to tell

17.

What is the inverse of an exponential function?

a)

polynomial function

b)

logarithmic function

c)

linear function

d)

quadratic function

18.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

19.

a)

A

b)

B

c)

C

d)

D

20.

If f(x) = ³√(x - 5) + 7, what is the inverse function?

a)

f^-1(x) = (x - 5)³ + 7

b)

f^-1(x) = ³√(x - 7) + 5

c)

f^-1(x) = 3x + 2

d)

f^-1(x) = (x - 7)³ + 5

21.

Which is f^-1(x)?

a)

f^-1(x)=4(x+3)³

b)

f^-1(x)=(4x+12)³

c)

f^-1(x)=3+1/4(x)³

d)

f^-1(x)=1/4(x+3)³

22.

Which graph represents f^-1(x) over the same domain?

a)

b)

c)

d)

23.

How must the domain of f(x) be restricted such that g(x)=f^-1(x) ?

a)

x ≤ 0

b)

x ≥ 0

c)

x ≤ 3

d)

x ≥ 3

24.

Graph the inverse

a)

b)

c)

d)

25.

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

a)

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

b)

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

c)

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

d)

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

26.

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?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

27.

If $f\left(3\right)\ =\ 12,\$ what is the value of $f^{-1}\left(12\right)$ ?

a)

48

b)

Not enough information

c)

3

d)

0

28.

Which of the following is the graph of the inverse?

a)

b)

c)

d)

29.

a)

a

b)

b

c)

c

d)

d

30.

What are you supposed to do Algebraically to verify that the two functions f(x) & g(x) are inverses of each other?

a)

Verify the f(g(x)) = x only

b)

Verify that g(f(x)) = x only

c)

Verify that BOTH f(g(x)) = x & g(f(x)) = x

31.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

32.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

33.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

34.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

35.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

36.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

37.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

38.

What is the test to determine if a graph represents a function?

a)

Horizontal line test

b)

Vertical line test

c)

Heidelberg Uncertainty Test

d)

Obi Wan Kenobi Test

39.

Does this mapping diagram represent a function?

a)

No, because there are repeating input values

b)

Yes, because there are no repeating input values

40.

What is the test to determine if a graph represents a ONE TO ONE function?

a)

Horizontal line test

b)

Vertical line test

c)

Heidelberg Uncertainty Test

d)

Obi Wan Kenobi Test

41.

a)

One-to-One Function

b)

Not One-to-One Function

42.

Determine which function is one-to-one?

a)

b)

c)

43.

$g(x)=𝑥^4+3$

a)

One-to-one Function

b)

Not One-to-one Function

44.

$h(x)=\frac{1}{(𝑥−2)}$

a)

One-to-one Function

b)

Not One-to-one Function

45.

$b(x)=𝑥^8+9$

a)

One-to-one Function

b)

Not One-to-one Function

46.

The following mapping is (a) because (b) .

Choose from the below words

a function

each input maps to exactly one output.

not a function

both a function and one-to-one

each output maps to exactly one input

neither the x's or y's repeat

47.

The following mapping is (a) because (b) .

Choose from the below words

both a function and one-to-one

neither the x's or y's repeat

not a function

each output maps to exactly one input

a function

each input maps to exactly one output.

48.

Find the inverse of $y=\ln\left(x+3\right)$

a)

$y=e^x-3$

b)

$y=e^{x-3}$

c)

$y=e^x+3$

d)

$y=e^{x+3}$

49.

Which is the inverse of the table?

a)

b)

c)

d)

50.

The domain of the square root function is [-3, inf) and its range is [5, inf). What is the RANGE of its inverse?

a)

[3, inf)

b)

[-3, inf)

c)

[5, inf)

d)

[-5, inf)

51.

What is g^-1(1)?

a)

1

b)

-1

c)

3

d)

-3

52.

What is h^-1(3)?

a)

5

b)

3

c)

7

d)

-3

2.8 - Inverse Functions

Total questions: 52

Worksheet time: 3hrs 36mins

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