Lebl-Basic-Analysis-I · Problem 3.6.15

Continuous Functions

Mathematics · monotone-functions-continuity

Problem

Suppose

f : (a, b) \to (c, d)

is a strictly increasing onto function. Prove that there exists a

g : (a, b) \to (c, d)

, which is also strictly increasing and onto, and

g(x) < f(x)

for all

x \in (a, b)