Which of the following functions is the inver | vedclass

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(A) function $f$ is the inverse of itself if $f(f(x)) = x$ for all $x$ in its domain.For option $A$,let $f(x) = \frac{1 - x}{1 + x}$.Then $f(f(x)) = f

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

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(A) function $f$ is the inverse of itself if $f(f(x)) = x$ for all $x$ in its domain.For option $A$,let $f(x) = \frac{1 - x}{1 + x}$.Then $f(f(x)) = f\left(\frac{1 - x}{1 + x}\right) = \frac{1 - \left(\frac{1 - x}{1 + x}\right)}{1 + \left(\frac{1 - x}{1 + x}\right)}$.Multiplying the numerator and denominator by $(1 + x)$,we get:$f(f(x)) = \frac{(1 + x) - (1 - x)}{(1 + x) + (1 - x)} = \frac{1 + x - 1 + x}{1 + x + 1 - x} = \frac{2x}{2} = x$.Since $f(f(x)) = x$,the function $f(x) = \frac{1 - x}{1 + x}$ is the inverse of itself.

Which of the following functions is the inverse of itself?

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