Step by step
The question
Question: find (f/g)(−3) for f(x) = 4x − 3 and g(x) = x + 1.
f(x) = 4x − 3
g(x) = x + 1
(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(−3)
Put −3 in place of x in f.
We write it in brackets.
f(−3) = 4(−3) − 3
Times comes before minus.
Order: ( ) → x² √ → × ÷ → + −
4(−3) = 4 × (−3)
+ × − = −
4(−3) means 4 times −3.
Plus times minus is minus.
4 times 3 is 12.
So we get −12.
= −12 − 3
Start at −12.
Go down 3.
We land on −15.
f(−3) = −15
2 Work out g(−3)
Put −3 in place of x in g.
g(−3) = −3 + 1
Start at −3.
Go up 1.
We land on −2.
g(−3) = −2
3 Divide them
Careful!
Before we divide, look at the bottom.
If g(−3) were 0, we could not divide at all.
Careful: the bottom g can never be 0
f(−3)/g(−3): −15 over −2.
So (f/g)(−3) = 15/2.
(f/g)(−3) = −15−2
4 Check
Let's check another way.
The whole rule: (f/g)(x) = (4x − 3)/(x + 1).
(f/g)(x) = 4x − 3x + 1
Put in −3: 15/2 again.
It works!
(f/g)(−3) = 4(−3) − 3(−3) + 1 = −15−2 = 152
Let's look back.
First: work out f(−3).
Then: work out g(−3).
Then: divide them.
Last: check.
Answer
(f/g)(−3) = −15−2