f(x) = 3x, g(x) = x + 4, find (f + g)(x)

Step by step

The question

Question: find (f + g)(x) for f(x) = 3x and g(x) = x + 4.

(f + g)(x) means f of x plus g of x.

We add the two answers.

1 Put the rules in

Each rule goes in brackets, as one piece: 3x + (x + 4).

2 Open the brackets

A bracket with a plus or nothing in front can just be removed.

Now we have 3x + x + 4.

3 Group like terms

Terms are the parts between the + and − signs.

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

All the x terms go together.

Each colour is one kind.

3x + x is 4x.

It is like 3 apples plus 1 apple: that is 4 apples.

So the expression is 4x + 4.

4 Check

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

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

Plus: 12.

Now our answer with x = 2.

We get 12 too.

It works!

Let's look back.

First: put the rules in.

Then: open the brackets.

Then: group like terms.

Last: check.