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  • Which of the following functions is inverse of itself in its domain?Option: 1 <img alt="f\left ( x \right )= \frac{1-x}{1+x}" src="https://learn.care

Which of the following functions is inverse of itself in its domain?

Option: 1

f\left ( x \right )= \frac{1-x}{1+x}


Option: 2

f\left ( x \right )= 5^{\log x}


Option: 3

f\left ( x \right )= 2^{x\left ( x-1 \right )}


Option: 4

None of these


Answers (1)

best_answer

As we learnt

INVERTIBLE FUNCTION

A function f : X → Y is defined to be invertible, if there exists a function g : Y → X such that gof=I_{x} and fog=I_{y}.

Now,

fof(x)=f(f(x))=f(\frac{1-x}{1+x})=\frac{1-\frac{1-x}{1+x}}{1+\frac{1-x}{1+x}}=x

so

 f\left ( x \right )= \frac{1-x}{1+x} is inverse of itself

 

Posted by

sudhir.kumar

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