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# 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)=x

^{2}is not invertiable since this is not one-to-one as (-x)^{2}=x^{2}.

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