Inverse of function of Set

The inverse of a one-to-one corresponding function f: A → B, is the function g: B → A, holding the following property −

f(x) = y ⇔ g(y) = x

The function f is called invertible if its inverse function g exists.

Example

• A Function f : Z → Z, f(x)=x+5, is invertible since it has the inverse function g : Z → Z, g(x)= x-5.

• A Function f : Z → Z, f(x)=x² is not invertiable since this is not one-to-one as (-x)²=x².