Lebl-Basic-Analysis-I · Problem 3.3.12

Continuous Functions

Mathematics · 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})