Question

Check the functions whose inverses are also functions.

On a coordinate plane, an absolute value function opens down.

On a coordinate plane, an exponential functions increases from quadrant 2 into quadrant 1.

On a coordinate plane, a cubic function has an x-intercept of (0, 0).

Answer 1

You need the function to be one-to-one (pass the horizontal‑line test) for its inverse to be a function.

- Absolute value opening down: No. A (downward) V is not one-to-one (horizontal lines meet it twice), so its inverse is not a function.
- Exponential increasing from Q2 into Q1: Yes. Exponentials are strictly monotonic, so they are one-to-one and their inverse (a logarithm) is a function.
- Cubic with x‑intercept (0,0): Not enough information. Some cubics (e.g. y = x^3) are one‑to‑one and have functional inverses; others with turning points are not. You must know whether the cubic is strictly monotonic to decide.