Lebl-Basic-Analysis-I · Problem 3.2.17

Continuous Functions

Mathematics · continuous-functions

Problem

Suppose

S \subset \mathbb{R}

and let

f : S \to \mathbb{R}

and

g : S \to \mathbb{R}

be continuous functions. Define

p : S \to \mathbb{R}

p(x) := \max\{f(x), g(x)\}

and

q : S \to \mathbb{R}

q(x) := \min\{f(x), g(x)\}

. Prove that

p

and

q

are continuous.