Question

Which of the following functions is inverse of itself?

विकल्प

• `f(x) = (1 - x)/(1 + x)`

• `g(x) = 5^(log x)`

• `h (x) = 2^(x(x - 1))`

• None of these 

Answer 1

`f(x) = (1 - x)/(1 + x)`

Explanation:

Since fof(x) = f(f(x))

= `f((1 - x)/(1 + x)) = (1 - ((1 - x)/(1 + x)))/(1 - ((1 - x)/(1 + x))` = x, for all x

So, inverse of f is f itself. It can be easily seen that gog (x) ≠ x and hoh (x) ≠ x