Step by step
The question
Question: find (f − g)(−2) for f(x) = 3x − 2 and g(x) = x + 6.
f(x) = 3x − 2
g(x) = x + 6
(f − g)(x) means f of x minus g of x.
We take away the two answers.
(f − g)(x) = f(x) − g(x)
1 Work out f(−2)
Put −2 in place of x in f.
We write it in brackets.
f(−2) = 3(−2) − 2
Times comes before minus.
Order: ( ) → x² √ → × ÷ → + −
3(−2) = 3 × (−2)
+ × − = −
3(−2) means 3 times −2.
Plus times minus is minus.
3 times 2 is 6.
So we get −6.
= −6 − 2
Start at −6.
Go down 2.
We land on −8.
f(−2) = −8
2 Work out g(−2)
Put −2 in place of x in g.
g(−2) = −2 + 6
Start at −2.
Go up 6.
We land on 4.
g(−2) = 4
3 Take away them
f(−2) minus g(−2): −8 − 4.
(f − g)(−2) = −8 − 4
So (f − g)(−2) = −12.
(f − g)(−2) = −12
4 Check
Let's check another way.
First the whole rule: (f − g)(x) = 2x − 8.
(f − g)(x) = 2x − 8
Then put in −2.
We get −12 again.
It works!
(f − g)(-2) = 2(−2) − 8 = −4 − 8 = −12
Let's look back.
First: work out f(−2).
Then: work out g(−2).
Then: take away them.
Last: check.
Answer
(f − g)(−2) = −12