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# Understand the problem

True or False? If $$f: \Bbb R \to \Bbb R$$ is differentiable and bijective then $$f^{-1}$$ is also differentiable.
##### Source of the problem
TIFR GS 2017 Entrance Examination Paper
Real Analysis
Easy
##### Suggested Book
Introduction to Real Analysis, Fourth Edition, English, Paperback, by Robert G. Bartle and Donald R. Sherbert. Introduction to Real Analysis, Seventh Edition, English, Paperback, by S. K. Mapa.

# Start with hints

Do you really need a hint? Try it first!

The given statement is a general statement. So, if I can find a function $$f(x)$$ which is differentiable and bijective on $$\Bbb R$$ but whose inverse function $$f^{-1}$$ is not differentiable then I would be able to show that the statement is not generally true. Now, can you find such a function?
Let us consider the function $$f(x) = x^3$$ . Can you now show that the function is contradicting the statement given to us?
The function $$f(x)= x^3$$ is a bijective and differentiable function. It’s inverse is $$x^{\frac{1}{3}}$$ which, you can see, is not differentiale at $$x=0$$. Hence the statement is false.

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