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Function Inverses Answers

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

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

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

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

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

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

one-fifth (one-fifth x + 5) + 5

One-fifth (5 x minus 25) + 5

StartFraction 1 Over (one-fifth x + 5) EndFraction

5 (one-fifth x + 5) + 5

Which function has an inverse that is also a function?

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

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

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

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

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))?

–6

–3

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

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

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

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

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

If and are inverse functions of each other and , what is ?

Option

Which function is the inverse of ?

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

Option

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

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

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

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

f(x) is not a function.

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

(0, –2)

(1, –1)

(2, 0)

(3, 3)

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

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.

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).

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).

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).

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