f(x) = x + 4, g(x) = 2x, find (f × g)(x) Step by Step

Step by step

The question

Question: find (f × g)(x) for f(x) = x + 4 and g(x) = 2x.

f(x) = x + 4

g(x) = 2x

(f × g)(x) means f of x times g of x.

We multiply the two answers.

(f × g)(x) = f(x) × g(x)

1 Put the rules in

Each rule goes in brackets, as one piece: (x + 4)(2x).

(f × g)(x) = (x + 4)(2x)

Careful!

Times is not putting one inside the other.

We multiply the two rules.

Careful: (f × g)(x) is not f(g(x))

2 Split the first bracket

Each part of the first bracket multiplies the whole second bracket.

(a + b)(c + d) = a(c + d) + b(c + d)

The parts of the first bracket are x and 4.

Each one takes the whole second bracket.

= x(2x) + 4(2x)

3 Open the brackets

What is in front of a bracket multiplies every part inside.

a(b + c) = ab + ac

So we write each part times what is in front.

= x(2x) + 4(2x)

x times 2x is 2x².

4 times 2x is 8x.

(f × g)(x) = 2x² + 8x

4 Check

Let's check with a number: x = 2.

f of 2 is 6, g of 2 is 4.

Times: 24.

f(2) × g(2) = 6 × 4 = 24

Now our answer with x = 2.

We get 24 too.

It works!

Answer: 2(2)² + 8(2) = 8 + 16 = 24

Let's look back.

First: put the rules in.

Then: split the first bracket.

Then: open the brackets.

Last: check.

Answer