Question

The following tables represent a function and its inverse. Compare the functions.

h(x)





h–1(x)



Which statements describe the functions? Check all that apply.

The domain of h–1(x) is the range of h(x).
The range of h–1(x) is the range of h(x).
The x-intercept of h–1(x) is the x-intercept of h(x).
The x-coordinate of the x-intercept of h–1(x) is the y-coordinate of the y-intercept of h(x).
The maximum of h(x) is the largest x-value of
h–1(x).

Answer 1

Correct answers: 1, 4, and 5.

Why:
- Statement 1: True. An inverse swaps inputs and outputs, so the domain of h^{-1} is the range of h.
- Statement 2: False. The range of h^{-1} is the domain of h, not the range of h.
- Statement 3: False. If h has x-intercept (a,0), the inverse has (0,a) (a y-intercept), so x-intercepts do not in general stay x-intercepts.
- Statement 4: True. If h^{-1} has x-intercept x* (i.e. (x*,0) on h^{-1}), then (0,x*) is on h, so x* equals the y-coordinate of h’s y-intercept.
- Statement 5: True. The maximum value of h (largest y) becomes the largest x-value among points of h^{-1}.