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Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 1 / 3E / iii / Solution

No. Take

f (x) = {x, 2 x, x \geq 0, x < 0, g (y) = {2 y, y, y \geq 0, y < 0.

Both functions are nonconstant on every interval and nondifferentiable at zero, but

g (f (x)) = 2 x

is differentiable.

Solved by gpt-5.6-sol high.

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