Counterexample for $f$ is strictly increasing ,$ g$ and $f\circ g$ is continous but f is not continous

Question

I wanted to find counterexample

Counterexample for $f$ is strictly increasing,$ g$ and $f\circ g$ is continuous but $f$ is not continuous

Where f and g are function form $[0,1]\to [0,1]$

How to approach to find such example

Any Help will be appreciated

Answer 1

Hint: Let $g(x)=0{}{}{}{}{}{}$.