Lebl-Basic-Analysis-I · Problem 3.2.14

Continuous Functions

Mathematics · continuous-functions

Problem

Suppose

f : [-1, 0] \to \mathbb{R}

and

g : [0, 1] \to \mathbb{R}

are continuous and

f(0) = g(0)

. Define

h : [-1, 1] \to \mathbb{R}

h(x) := f(x)

x \leq 0

and

h(x) := g(x)

x > 0

. Show that

h

is continuous.