Basic Analysis I — Real Analysis · Problem 3.2.9

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · continuous-functions

Problem

Give an example of functions

f : \mathbb{R} \to \mathbb{R}

and

g : \mathbb{R} \to \mathbb{R}

such that the function

h

, defined by

h(x) := f(x) + g(x)

, is continuous, but

f

and

g

are not continuous. Can you find

f

and

g

that are nowhere continuous, but

h

is a continuous function?