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

This is true. If $x_n\to x$, continuity of $g$ gives $g(x_n)\to g(x)$, and continuity of $f$ then givesEquivalently, this is the composition of continuous functions theorem.

Solved by gpt-5.6-sol high.