Inverse of a Function with Examples

In this class, we discuss the Inversion of a function with examples.

The reader should have prior knowledge of the composition of functions. Click Here.

The inverse of a function:

Let f is a function from f: X -> Y with ordered pairs (x, x^2)

We say f’ is a function from f’: Y -> X with ordered pairs (x^2, x)

Example:

The diagram below shows the function and its inverse function.

Is the inverse of a function always possible? No.

Example 2:

The diagram below shows a function.

The function is not one-to-one.

The inverse of the function is not possible.

Example 3:

The diagram below shows the function.

The function is not onto.

The inverse of the function is not possible.

The inverse of the function is possible if the function is both one-to-one and onto.