Question

Consider the function and its inverse, .

Which statement describes how the x-intercept for the original function can be determined?

The x-intercept for f(x) is the constant in the f(x) equation.
The x-intercept for f(x) is the constant in the f–1(x) equation.
The x-intercept for f(x) is the reciprocal of the constant in the f(x) equation.
The x-intercept for f(x) is the reciprocal of the constant in the f–1(x) equation.

Answer 1

"The x-intercept for f(x) is the constant in the f–1(x) equation."

Reason: if f(a) = 0, then f^{-1}(0) = a. So the x‑intercept a of f is the value of f^{-1} at 0 — the constant (y‑intercept) term in the equation for f^{-1}.