Question Of The Day

If y = f (x), and f (x²) = (1 – x²)/(1 + x²), then which of the following is true?  

a) x = f (2y) – 1

b) f (1/x²) = f(x²)

c) f(2x²) = f(x²) – 1          

d) x = f(y)

Ans: d) x = f(y)

f (x²) = (1 – x²)/(1 + x²). ∴ y = f(x) = (1 – x)/(1 + x). Solving, we get x = (1 – y)/(1 + y). ∴ x= f(y).