Question

A differentiable function f satisfies the relation f((x + y)/(1 + xy)) = f(x).f(y) for all x, y in R – {–1}, where f(0) ≠ 0 and f'(0) = 1. Find f(x).

Answer 1

Clearly, f(0) = 1

We have,

Integrating, 

we get

which is the required solution.