Let be a continuous function,

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)

be a continuous function,

\forall x \in \mathbb{R}

,

f(0)=1

and

f(x)\neq x

for any

x\in \mathbb{R}

, then show

f(f(x))>x,\ \forall x\in \mathbb{R}

.

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