How to Find the Inverse of a Function

Finding the Inverse of a Function

An inverse function is a function that reverses another function.

If we have a function f(x), we can find the inverse function f−1(x).

How to Find the Inverse of a Function

Finding the inverse of a function is easy.

Question

Find the inverse function of the function below.

Step-by-Step:

1

Rearrange the function to find "x =".

f(x) = ½x + 1
f(x) − 1 = ½x + 1 − 1 Subtract 1 from both sides
f(x) − 1 = ½x
2 × ( f(x) − 1 ) = 2 × ½x Multiply both sides by 2
2( f(x) − 1 ) = x
x = 2( f(x) − 1 )

We have rearranged f(x) = ½x + 1 to find what "x = ".

x = 2( f(x) − 1 )

2

Replace x with f−1(x).

f−1(x) = 2( f(x) − 1 )

3

Replace f(x) with x.

f−1(x) = 2( x − 1 )

Answer:

The inverse of the function f(x) = ½x + 1 is:

f−1(x) = 2(x − 1).

Slider

The slider below explains more about how to find the inverse of a function.

Open the slider in a new tab

See Also

What is a function? What are Cartesian coordinates?