Step by step
The question
Question: find (f × g)(−1) for f(x) = x + 4 and g(x) = 2x − 1.
f(x) = x + 4
g(x) = 2x − 1
(f × g)(x) means f of x times g of x.
We multiply the two answers.
(f × g)(x) = f(x) × g(x)
1 Work out f(−1)
Put −1 in place of x in f.
f(−1) = −1 + 4
Start at −1.
Go up 4.
We land on 3.
f(−1) = 3
2 Work out g(−1)
Put −1 in place of x in g.
We write it in brackets.
g(−1) = 2(−1) − 1
Times comes before minus.
Order: ( ) → x² √ → × ÷ → + −
2(−1) = 2 × (−1)
+ × − = −
2(−1) means 2 times −1.
Plus times minus is minus.
2 times 1 is 2.
So we get −2.
= −2 − 1
Start at −2.
Go down 1.
We land on −3.
g(−1) = −3
3 Multiply them
f(−1) times g(−1): 3 × (−3).
(f × g)(−1) = 3 × (−3)
So (f × g)(−1) = −9.
(f × g)(−1) = −9
4 Check
Let's check another way.
First the whole rule: (f × g)(x) = 2x² + 7x − 4.
(f × g)(x) = 2x2 + 7x − 4
Then put in −1.
We get −9 again.
It works!
(f × g)(-1) = 2(−1)2 + 7(−1) − 4 = 2 − 7 − 4
= −9
Let's look back.
First: work out f(−1).
Then: work out g(−1).
Then: multiply them.
Last: check.
Answer
(f × g)(−1) = −9