A bijective function satisfies for every with some function

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

A bijective function

f:\mathbb R\to\mathbb R

satisfies

(g\circ f)(x)=x

for every

x\in\mathbb R

with some function

g

. Is this single condition sufficient to conclude that

g=f^{-1}

? Give a brief reason.

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