f(x) = x + 5, g(x) = 2x - 1, find (f + g)(x) Step by Step

Step by step

The question

Question: find (f + g)(x) for f(x) = x + 5 and g(x) = 2x − 1.

f(x) = x + 5

g(x) = 2x − 1

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

We add the two answers.

(f + g)(x) = f(x) + g(x)

1 Put the rules in

Each rule goes in brackets, as one piece: (x + 5) + (2x − 1).

(f + g)(x) = (x + 5) + (2x − 1)

2 Open the brackets

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

( ) away

Now we have x + 5 + 2x − 1.

= x + 5 + 2x − 1

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.

Plain numbers go together.

Each colour is one kind.

like terms = same letters,

same powers

We move like terms next to each other.

Each term takes its sign with it.

= x + 2x + 5 − 1

x + 2x is 3x.

It is like 1 apple plus 2 apples: that is 3 apples.

5 − 1 is 4.

x + 2x = 3x

5 − 1 = 4

So the expression is 3x + 4.

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

4 Check

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

f of 2 is 7, g of 2 is 3.

Plus: 10.

f(2) + g(2) = 7 + 3 = 10

Now our answer with x = 2.

We get 10 too.

It works!

Answer: 3(2) + 4 = 6 + 4 = 10

Let's look back.

First: put the rules in.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer