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TIFR-2017-Maths-B: 2

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Let $f$ be a continuous function on $\mathbb{R}$ satisfying the relation

$$f\left ( f\left ( f\left ( x \right ) \right ) \right )=x \:for\:all \:x \in \mathbb{R}.$$

Prove or disprove that $f$ is the identity function.
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