Basic Analysis I — Real Analysis · Problem 3.3.9

Continuous Functions — Jiri Lebl

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

Problem

(Challenging) Suppose

f(x)

is a bounded polynomial, in other words, there is an

M

such that

\bigl|f(x)\bigr| \leq M

for all

x \in \mathbb{R}

. Prove that

f

must be a constant.