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 Incoming links: Composition of continuous functions

Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 1 / 9F / b / i / Solution Created 2026-09-24 Updated 2026-10-03

True. If

x_{n} \to x

, continuity of

g

gives

g (x_{n}) \to g (x)

, and continuity of

f

then gives

f (g (x_{n})) \to f (g (x)) .

Equivalently, this is the composition of continuous functions theorem.

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