Solve f(x) = 2x - 3, f(f(x)) Step by Step

Step by step

The question

Question: find f(f(x)) for f(x) = 2x − 3.

f(x) = 2x − 3

1 Work out the inside

f(f(x)) is a function inside a function.

Like with brackets, we start inside.

First f(x).

inside first: f(x)

f(x) is 2x − 3.

So f(f(x)) is f(2x − 3).

f(f(x)) = f(2x − 3)

2 Put it in

Put (2x − 3) in place of every x in f.

We keep it in brackets.

= 2(2x − 3) − 3

3 Open the brackets

The 2 in front of the bracket multiplies every part inside.

a(b + c) = ab + ac

So we write 2 times each part.

= 2(2x) + 2(−3) − 3

− × + = −

Watch the signs.

2 times 2x is 4x.

2 times (−3) is −6.

= 4x − 6 − 3

4 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

Plain numbers go together.

Each colour is one kind.

like terms = same letters,

same powers

−6 − 3 is −9.

−6 − 3 = −9

So the expression is 4x − 9.

f(f(x)) = 4x − 9

5 Check

Let's check.

We pick a number for each letter: x = 2.

We put it into the start.

Start: 2 × (2 × 2 − 3) − 3 = 2 × 1 − 3

= 2 − 3 = −1

Now into our answer.

Answer: 4 × 2 − 9 = 8 − 9 = −1

Both give −1.

Same value, so 4x − 9 is right!

Both give −1

Let's look back.

First: work out the inside.

Then: put it in.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer