Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 1 / 10E / c / ii / Solution

No. At $a=0$, letThe function $g$ is differentiable at $f(0)=0$, andso the composite has derivative one at zero. Butis unbounded, so $f$ is not differentiable. This is a nondifferentiable inner function with a differentiable nondegenerate composite.

Solved by gpt-5.6-sol high.