Step by step
The question
Question: find (f/g)(4) for f(x) = 2x + 1 and g(x) = x − 2.
f(x) = 2x + 1
g(x) = x − 2
(f/g)(x) means f of x divided by g of x.
We write it as a fraction: f on top, g at the bottom.
(f/g)(x) = f(x)g(x)
1 Work out f(4)
Put 4 in place of x in f.
We write it in brackets.
f(4) = 2(4) + 1
Times comes before plus.
Order: ( ) → x² √ → × ÷ → + −
2(4) = 2 × 4
2(4) means 2 times 4.
2 times 4 is 8.
= 8 + 1
8 plus 1 is 9.
f(4) = 9
2 Work out g(4)
Put 4 in place of x in g.
g(4) = 4 − 2
4 minus 2 is 2.
g(4) = 2
3 Divide them
Careful!
Before we divide, look at the bottom.
If g(4) were 0, we could not divide at all.
Careful: the bottom g can never be 0
f(4)/g(4): 9/2.
So (f/g)(4) = 9/2.
(f/g)(4) = 92
4 Check
Let's check another way.
The whole rule: (f/g)(x) = (2x + 1)/(x − 2).
(f/g)(x) = 2x + 1x − 2
Put in 4: 9/2 again.
It works!
(f/g)(4) = 2(4) + 14 − 2 = 92 = 92
Let's look back.
First: work out f(4).
Then: work out g(4).
Then: divide them.
Last: check.
Answer
(f/g)(4) = 92