f(x) = 2x^2, find x when f(x) = 18

Step by step

The question

Question: find x when f(x) = 18 for f(x) = 2x².

f(x) = 18 means: the answer that comes out is 18.

We look for the x that goes in.

Careful!

It is not f(18).

18 is what comes out, not what goes in.

1 Write the equation

f(x) is 2x².

So 2x² = 18.

Now we solve it.

2 Get x² alone

To remove times 2, we divide both sides by 2.

18 divided by 2 is 9.

3 Square root of both sides

x squared is 9.

So x is the square root of 9, or minus it.

Minus times minus is plus, so the negative one works too.

3 times 3 is 9.

So x = 3 or x = −3.

4 Check

Let's check: put 3 into f.

We get 18.

And −3 into f.

We get 18 too.

So f(3) = 18 and f(−3) = 18.

Both answers are right!

Let's look back.

First: write the equation.

Then: get x² alone.

Then: square root of both sides.

Last: check.