Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 1 / 12E / f / Solution

True. If $|f(x_0)|>C$, continuity gives an interval of positive length on which $|f|>C+\delta$. Its $L^p$ norm exceeds $(C+\delta ){\ell }^{1/p}$, which tends to $C+\delta >C$ as $p\to \infty$, a contradiction.

Solved by gpt-5.6-sol high.