(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is to prove that:

if

f(g(x))=x ........... (1)

and

g(f(x))=x ............(2)

then f(x)=g^{-1}(x)

3. The attempt at a solution

Differentiating (1) wrt x

f'(g(x))*g'(x)=1

f'(g(x))=1/g'(x)

As the slopes are reciprocals of each other, hence f(x)=g^{-1}(x)

Is this as simple as it seems? Are there any possible exceptions?

Is there any more explanatory proof????

Please help me.

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# Homework Help: Inverse Function

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