Working out the inverse function (inverse functions)

The inverse function f⁻¹(x) is a reflection of f(x) in the mirror line y = x. To work out the inverse function follow these steps:

Step 1: Change f(x) for x and x for f⁻¹(x).

Step 2: Make f⁻¹(x) the subject.

Let’s run through a few examples:

Example 1

Work out the inverse function if f(x) = 9x + 1

Step 1: Change f(x) for x and x for f⁻¹(x).

f(x) = 9x + 1

x = 9f⁻¹(x) + 1

Step 2: Make f⁻¹(x) the subject.

x = 9f⁻¹(x) + 1

Take 1 off both sides

x – 1 = 9f⁻¹(x)

Divide both sides by 9.

(x-1)/9 = f⁻¹(x)

So our final inverse function is:

f⁻¹(x) = (x-1)/9

Example 2

Work out the inverse function if f(x) = 2x - 2

Step 1: Change f(x) for x and x for f⁻¹(x).

f(x) = 2x – 2

x = 2f⁻¹(x) - 2

Step 2: Make f⁻¹(x) the subject.

x = 2f⁻¹(x) - 2

Add 2 to both sides

x + 2 = 2f⁻¹(x)

Multiply both sides by 3.

3x + 6 = f⁻¹(x)

So our final inverse function is:

f⁻¹(x) = 3x + 6

Example 3

Work out the inverse function if f(x) = 1/x + 8

Step 1: Change f(x) for x and x for f⁻¹(x).

f(x) = 1/x + 8

x = 1/ f⁻¹(x) + 8

Step 2: Make f⁻¹(x) the subject.

x = 1/ f⁻¹(x) + 8

Take 8 from both sides.

x -8 = 1/f⁻¹(x)

Take the reciprocal of both sides

1/(x-8) = f⁻¹(x)

So our final inverse function is:

f⁻¹(x) = 1/(x-8)

For some more questions on inverse functions try these links:

Alternative method for finding the inverse function.

Trickier inverse function examples.

More by this Author


Comments

No comments yet.

    0 of 8192 characters used
    Post Comment

    No HTML is allowed in comments, but URLs will be hyperlinked. Comments are not for promoting your articles or other sites.


    Click to Rate This Article
    working