Function Inverses Answers

1

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Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function?

A

The graph of h(x) passes the vertical line test.

B

The graph of the inverse of h(x) is a vertical line.

C

The graph of the inverse of h(x) passes the horizontal line test.

D

The graph of h(x) passes the horizontal line test.

2

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Which function has an inverse that is also a function?

A

{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}

B

{(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}

C

{(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}

D

{(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

3

Which function has an inverse that is a function?

A

b(x) = x2 + 3

B

d(x) = –9

C

m(x) = –7x

D

p(x) = |x|

4

Which function is the inverse of ?

A

f Superscript negative 1 Baseline (x) = one-half x minus three-halves

B

mc013-3.jpg

C

mc013-4.jpg

D

mc013-5.jpg

5

If and , which expression could be used to verify that is the inverse of ?

A

one-third (one-third x)

B

Option

C

Option

D

Option

6

Which function has an inverse that is also a function?

A

{(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)}

B

{(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}

C

{(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

D

{(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

8

Which graph shows a function whose inverse is also a function?

A

On a coordinate plane, 2 curves are shown. f (x) is a curve that starts at (0, 0) and opens down and to the right in quadrant 1. The curve goes through (4, 2). The inverse of f (x) starts at (0, 0) and curves up sharply and opens to the left in quadrant 1. The curve goes through (2, 4).

B

On a coordinate plane, 2 parabolas are shown. f (x) opens up and goes through (negative 2, 5), has a vertex at (0, negative 2), and goes through (2, 5). The inverse of f (x) opens right and goes through (5, 2), has a vertex at (negative 2, 0), and goes through (5, negative 2).

C

On a coordinate plane, two v-shaped graphs are shown. f (x) opens down and goes through (0, negative 3), has a vertex at (1, 3), and goes through (2, negative 3). The inverse of f (x) opens to the left and goes through (negative 3, 2), has a vertex at (3, 1), and goes through (negative 3, 0).

D

On a coordinate plane, two curved graphs are shown. f (x) sharply increases from (negative 1, negative 4) to (0, 2) and then changes directions and curves down to (1, 1). At (1, 1) the curve changes directions and curves sharply upwards. The inverse of f (x) goes through (negative 4, negative 1) and gradually curves up to (2, 0). At (2, 0) the curve changes directions sharply and goes toward (1, 1). At (1, 1), the curve again sharply changes directions and goes toward (3, 1).

9

If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

A

(0, –2)

B

(1, –1)

C

(2, 0)

D

(3, 3)

10

If , what is ?

A

mc002-3.jpg

B

mc002-4.jpg

C

mc002-5.jpg

D

mc002-6.jpg

11

The function f(x) is shown below.xf(x)–61–32255380If g(x) is the inverse of f(x), what is the value of f(g(2))?

A

–6

B

–3

C

2

D

5

12

If and , which expression could be used to verify that is the inverse of ?

A

one-third (one-third x)

B

mc010-6.jpg

C

mc010-7.jpg

D

mc010-8.jpg

13

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

A

On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).

B

On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).

C

On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).

D

On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).

14

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

A

On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).

B

On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).

C

On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).

D

On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).

15

Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?

A

The graph of f(x) passes the vertical line test.

B

f(x) is a one-to-one function.

C

The graph of the inverse of f(x) passes the horizontal line test.

D

f(x) is not a function.

16

Which function is the inverse of ?

A

f Superscript negative 1 Baseline (x) = one-half x minus three-halves

B

Option

C

Option

D

Option

17

Which graph shows a function whose inverse is also a function?

A

On a coordinate plane, two curved graphs are shown. f (x) sharply increases from (negative 0.5, negative 5) to (0, negative 2) and then sharply changes directions and curves down to (0.5, 4.5). The curve then sharply changes direction and goes up through (1, 0). The inverse of f (x) curves slightly up from (negative 5, negative 1) to (negative 2, 0). The curve then sharply changes directions and go to the left toward (negative 3.5, 1). The curve then changes directions and goes through (0, 1) and gradually increases.

B

On a coordinate plane, 2 parabolas are shown. f (x) opens down and goes through (negative 1, negative 5), has a vertex at (0, 1), and goes through (1, negative 5). The inverse of f (x) opens to the left and goes through (negative 5, 1), has a vertex at (1, 0), and goes through (negative 5, negative 1).

C

On a coordinate plane, 2 lines are shown. f (x) has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). The inverse of f (x) has a positive slope and goes through (negative 2, negative 2), (negative 1, 0), and (0, 2).

D

On a coordinate plane, 2 v-shaped graphs are shown. f (x) opens up and goes through (negative 1, 5), has a vertex at (1, 1), and goes through (3, 5). The inverse of f (x) opens right and goes through (5, 3), has a vertex at (1, 1), and goes through (3, 0).

18

Which function has an inverse that is also a function?

A

{(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)}

B

{(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}

C

{(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

D

{(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

19

Which graph shows a function whose inverse is also a function?

A

On a coordinate plane, two curved graphs are shown. f (x) sharply increases from (negative 0.5, negative 5) to (0, negative 2) and then sharply changes directions and curves down to (0.5, 4.5). The curve then sharply changes direction and goes up through (1, 0). The inverse of f (x) curves slightly up from (negative 5, negative 1) to (negative 2, 0). The curve then sharply changes directions and go to the left toward (negative 3.5, 1). The curve then changes directions and goes through (0, 1) and gradually increases.

B

On a coordinate plane, 2 parabolas are shown. f (x) opens down and goes through (negative 1, negative 5), has a vertex at (0, 1), and goes through (1, negative 5). The inverse of f (x) opens to the left and goes through (negative 5, 1), has a vertex at (1, 0), and goes through (negative 5, negative 1).

C

On a coordinate plane, 2 lines are shown. f (x) has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). The inverse of f (x) has a positive slope and goes through (negative 2, negative 2), (negative 1, 0), and (0, 2).

D

On a coordinate plane, 2 v-shaped graphs are shown. f (x) opens up and goes through (negative 1, 5), has a vertex at (1, 1), and goes through (3, 5). The inverse of f (x) opens right and goes through (5, 3), has a vertex at (1, 1), and goes through (3, 0).

20

If and , which expression could be used to verify g(x) is the inverse of f(x)?