If f(x) = \(\rm \displaystyle {1-x\over1+x}\), then f^-1(x) = ?

Concept:

Functions:

If y = f(x), then we say that x = f^-1(y).

Calculation:

Let y = f(x) = \(\rm\displaystyle{1-x\over1+x}\).

⇒ y(1 + x) = 1 - x

⇒ y + xy = 1 - x

⇒ xy + x = 1 - y

⇒ x(1 + y) = 1 - y

⇒ x = \(\rm\displaystyle{1-y\over1+y}\) = f^-1(y)

Replacing y by x, we can say that:

f-1(x) = \(\rm\displaystyle{1-x\over1+x}\).