Step by step
The question
Question: find (f/g)(3) for f(x) = x² + 1 and g(x) = x + 1.
f(x) = x2 + 1
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.
f(3) = 32 + 1
Powers come before plus.
Order: ( ) → x² √ → × ÷ → + −
3² means 3 times 3.
32 = 3 × 3 = 9
That is 9.
= 9 + 1
9 plus 1 is 10.
f(3) = 10
2 Work out g(3)
Put 3 in place of x in g.
g(3) = 3 + 1
3 plus 1 is 4.
g(3) = 4
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): 10/4.
(f/g)(3) = 104
We make it simpler: 5/2.
(f/g)(3) = 52
4 Check
Let's check another way.
The whole rule: (f/g)(x) = (x² + 1)/(x + 1).
(f/g)(x) = x2 + 1x + 1
Put in 3: 5/2 again.
It works!
(f/g)(3) = 32 + 13 + 1 = 104 = 52
Let's look back.
First: work out f(3).
Then: work out g(3).
Then: divide them.
Last: check.
Answer
(f/g)(3) = 52