Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 1 / 9F / b / ii / Solution

This can be false because a strictly increasing $g$ need not be surjective. TakeThen $g$ is strictly increasing and $f\circ g=0$ is continuous, while $f$ is discontinuous at zero.

Solved by gpt-5.6-sol high.