Basic Analysis I — Real Analysis · Problem 3.3.12

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · extreme-and-intermediate-value-theorems

Problem

Suppose

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

is continuous such that

x \leq f(x) \leq x + 1

for all

x \in \mathbb{R}

. Find

f(\mathbb{R})