Discussion
Which of the following functions is inverse of itself ?
Answer: A
The function \(f(x)=\frac{1-x}{1+x}\) is its own inverse.
A function is its own inverse when f(f(x)) = x. Substituting:
\[ \begin{aligned} f(f(x)) &= \frac{1 - \frac{1-x}{1+x}}{1 + \frac{1-x}{1+x}} \\ &= \frac{(1+x) - (1-x)}{(1+x) + (1-x)} \\ &= \frac{2x}{2} = x \end{aligned} \]
5log x and 2x(x-1) do not return x when applied twice; the second is not even one-to-one. Since option A works, 'None of these' is wrong.
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