f(x) = x - 4, find x when f(x) = -1

Step by step

The question

Question: find x when f(x) = −1 for f(x) = x − 4.

f(x) = −1 means: the answer that comes out is −1.

We look for the x that goes in.

Careful!

It is not f(−1).

−1 is what comes out, not what goes in.

1 Write the equation

f(x) is x − 4.

So x − 4 = −1.

Now we solve it.

2 Remove the − 4

We want x by itself.

The − 4 is in the way.

To remove − 4, we add 4.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

− 4 and + 4 make zero.

Cross them out.

−1 + 4 = 3.

So x = 3!

3 Check

Let's check: put 3 into f.

We get −1.

So f(3) = −1.

x = 3 is right!

Let's look back.

First: write the equation.

Then: remove the − 4.

Last: check.