Question

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

Explanation:

A function's inverse is also a function if and only if the original function is one-to-one (passes the Horizontal Line Test: no horizontal line intersects the graph more than once). The top graph's function \(f(x)\) is strictly increasing, so it passes the Horizontal Line Test, meaning its inverse \(f^{-1}(x)\) (which is also strictly increasing) is a function. The bottom graph fails the Horizontal Line Test, as horizontal lines would intersect it multiple times, so its inverse would not be a function.

Answer:

The top graph (with \(f(x)\) and \(f^{-1}(x)\) as the curved and straight increasing lines)