Question

If f is one-one onto and differentiable on R. then
$(f {}^{ - 1} )(6) = 1 \div f(6)$

True or false ? if so give reason for your answer in the form of short proof or a counter example.

spam answer will be deleted on the spot.​

Answer 1

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False, because ${f}^{-1}$ here does not denote the f raise to the power -1, rather it is a inverse of a function which means when you put certain values in inverse function, you will get the pre-image of a function.

For instance,

Suppose f(x)=${x}^{2}$

Then it's ${f}^{-1}(x)=\sqrt{x}$

Now, let feed the values.

x=6

f(6)=${6}^{2}=36$

${f}^{-1}(6)={\sqrt{6}}≠\frac{1}{f(6)}$

Because,$\frac{1}{f(6)}=\frac{1}{36}$

This is the best possible answer

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Answer 2

Answer:

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