Inverse Function

A function, f, is the inverse of another , f−1, if:

f(a) = b, and f−1(b) = a.

Inverse Function

Note that:

The domain f−1 is the range of f.

The range of f−1 is the domain of f.

To find the range of a function we have to find the domain of its inverse function.

If two functions are the inverse of each other, their composition is the identity function.

(f o f −1) (x) = (f −1 o f) (x) = x

The graphs of f and f −1 are symmetrical about the bisector of the first and third quadrant.

Inverse Functions Graph

We must distinguish between the inverse function, f−1(x), and the inverse of a function, Inverse of a Function.

Calculation of the Inverse Function

1.Write the equation of the function with x and y.

2.Work out the value of the variable x as a function of the variable y.

3.The variables are exchanged.

Examples

Calculate the inverse function of:

Inverse Function Example

Inverse Function Operations

Inverse Function Operations

Inverse Function Operations

Inverse Function Operations

Check the result for x = 2.

Inverse Function Operations

Inverse Function


Inverse Function Example

Inverse Function Operations

Inverse Function


Inverse Function Example

Inverse Function Operations

No Function