Step by step
The question
Question: find (f − g)(3) for f(x) = 5x and g(x) = x − 2.
f(x) = 5x
g(x) = x − 2
(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(3)
Put 3 in place of x in f.
We write it in brackets.
f(3) = 5(3)
5(3) = 5 × 3
5(3) means 5 times 3.
5 times 3 is 15.
f(3) = 15
2 Work out g(3)
Put 3 in place of x in g.
g(3) = 3 − 2
3 minus 2 is 1.
g(3) = 1
3 Take away them
f(3) minus g(3): 15 − 1.
(f − g)(3) = 15 − 1
So (f − g)(3) = 14.
(f − g)(3) = 14
4 Check
Let's check another way.
First the whole rule: (f − g)(x) = 4x + 2.
(f − g)(x) = 4x + 2
Then put in 3.
We get 14 again.
It works!
(f − g)(3) = 4(3) + 2 = 12 + 2 = 14
Let's look back.
First: work out f(3).
Then: work out g(3).
Then: take away them.
Last: check.
Answer
(f − g)(3) = 14