Step by step
The question
Question: find f(−5) for f(x) = (x + 2)².
f(x) = (x + 2)2
f(x) is read "f of x".
It is a rule, called a function.
A number goes in for x.
The rule gives one answer out.
f(x) = "f of x"
x goes in → an answer comes out
1 Put the number in
f(−5) means: put −5 in place of every x.
We write it in brackets.
The brackets keep the minus with the number.
f(−5) = (−5 + 2)2
2 Brackets first
Brackets come first.
Order: ( ) → x² √ → × ÷ → + −
Start at −5.
Go up 2.
We land on −3.
= (−3)2
3 Powers
(−3)² means −3 times −3.
Minus times minus is plus.
(−3)2 = (−3) × (−3) = 9
That is 9.
f(−5) = 9
So f(−5) = 9.
Let's look back.
First: put the number in.
Then: brackets first.
Last: powers.
Answer
f(−5) = 9