Step by step
The question
Question: find (f/g)(2) 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(2)
Put 2 in place of x in f.
We write it in brackets.
f(2) = 2(2) + 1
Times comes before plus.
Order: ( ) → x² √ → × ÷ → + −
2(2) = 2 × 2
2(2) means 2 times 2.
2 times 2 is 4.
= 4 + 1
4 plus 1 is 5.
f(2) = 5
2 Work out g(2)
Put 2 in place of x in g.
g(2) = 2 − 2
2 minus 2 is 0.
g(2) = 0
3 Divide them
Careful!
Before we divide, look at the bottom.
If g(2) were 0, we could not divide at all.
Careful: the bottom g can never be 0
g(2) = 0.
We can never divide by 0.
So there is no answer: (f/g)(2) is not defined.
(f/g)(2) = 50
x = 2 makes g(x) = 0: no answer
Let's look back.
First: work out f(2).
Then: work out g(2).
Last: divide them.
Answer
x = 2 makes g(x) = 0: no answer