f(x) = 2x + 1, g(x) = x - 3, find (f + g)(x) Step by Step

Step by step

The question

Question: find (f + g)(x) for f(x) = 2x + 1 and g(x) = x − 3.

f(x) = 2x + 1

g(x) = x − 3

(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: (2x + 1) + (x − 3).

(f + g)(x) = (2x + 1) + (x − 3)

2 Open the brackets

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

( ) away

Now we have 2x + 1 + x − 3.

= 2x + 1 + x − 3

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.

= 2x + x + 1 − 3

2x + x is 3x.

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

1 − 3 is −2.

2x + x = 3x

1 − 3 = −2

So the expression is 3x − 2.

(f + g)(x) = 3x − 2

4 Check

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

f of 2 is 5, g of 2 is −1.

Plus: 4.

f(2) + g(2) = 5 + (−1) = 4

Now our answer with x = 2.

We get 4 too.

It works!

Answer: 3(2) − 2 = 6 − 2 = 4

Let's look back.

First: put the rules in.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer