Chapter 3 review Inverse Functions

If a given function f(x) has an inverse function f⁻¹(x), which of the following statements is true?

• If (a, b) is on the graph of f(x), then the graph of f⁻¹(x) must contain (−a, −b).

• If (a, b) is on the graph of f(x), then the graph of f⁻¹(x) must contain (−b, −a).

• If f(x) has an x-intercept at (c, 0), then the x-intercept of f⁻¹(x) must be (c, 0).

• If f(x) has an x-intercept at (c, 0), then the y-intercept of f⁻¹(x) must be (0, c).

The table below contains values of the function f(x). Which of the following tables represents f⁻¹(x)?

• Table A

• Table B

• Table C

• Table D

• The domain of f(x) must be restricted to {x | x ≥ 0}.

• The domain of f(x) must be restricted to {x | x ≤ 0}.

• The domain of f(x) must be restricted to {x | x ≥ -2}.

• The domain of f(x) must be restricted to {x | x ≤ -2}.

• (-∞, d)

• (d, ∞)

• (-∞, ∞)

• The domain of the inverse cannot be determined.

• A.

• B.

• C.

• D.

If the graph represents an exponential function, what is the equation of the vertical asymptote of its inverse logarithmic function?

• x = 0

• x = -2

• y = 0

• y = -2

What point do all three functions represented in the tables below have in common?

• maximum value

• minimum value

• x-intercept

• y-intercept

Which statement best describes the domain of f(x)?

• The domain of f(x) is the same as the domain of both g(x) and h(x).

• The domain of f(x) is the same as the range of both g(x) and h(x).

• The domain of f(x) contains all the real numbers greater than zero.

• The domain of f(x) contains all the real numbers less than zero.

• (0, 5)

• (1, 2)

• (2, 3)

• (3, 1)

If a given function f(x) has an inverse function, which of the following statements is true?

• If (a, b) is on the graph of f(x), then the graph of the inverse must contain (-b, -a).

• If f(x) has a y-intercept at (0, c), then the x-intercept of the inverse must be (c, 0).

• Both f(x) and its inverse must have the same domain.

• Both f(x) and its inverse must have the same y-intercept.