Inverse of f(x) = x + 4 Step by Step

Step by step

The question

Question: find the inverse of f(x) = x + 4.

f(x) = x + 4

The inverse function goes back.

If f takes 2 to 6, the inverse takes 6 back to 2.

inverse = goes back

f: 2 → 6 f ⁻¹: 6 → 2

1 Write y for f(x)

f(x) is the answer that comes out.

Let's call it y.

y = x + 4

2 Swap x and y

The inverse goes back: the answer goes in, and the start comes out.

So x and y swap places.

x = y + 4

Now we find y again, like in any formula.

3 y on the left

y is on the right.

We swap the two sides, so y is on the left.

They are still equal.

y + 4 = x

4 Remove the + 4

We want y by itself.

The 4 is in the way.

To remove 4, we take away 4.

We do it on both sides.

y ~~+ 4 − 4~~ = x − 4

They make zero.

Cross them out.

So y = x − 4.

y = x − 4

5 Write the inverse

This y is the inverse.

We write it f⁻¹(x).

f ⁻¹(x) = x − 4

The little −1 is part of the name.

It is not a power.

the −1 is a name,

not a power

6 Check

Let's check with a number.

Put 2 into f.

We get 6.

f(2) = 2 + 4 = 6

Now put 6 into the inverse.

We get 2.

f ⁻¹(6) = 6 − 4 = 2

The inverse took 6 back to 2.

So f⁻¹(x) = x − 4 is right!

Let's look back.

First: write y for f(x).

Then: swap x and y.

Then: y on the left.

Then: remove the + 4.

Then: write the inverse.

Last: check.

Answer