Step by step
The question
Question: find f(−2) for f(x) = x³ − 2x.
f(x) = x3 − 2x
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(−2) means: put −2 in place of every x.
We write it in brackets.
The brackets keep the minus with the number.
f(−2) = (−2)3 − 2(−2)
2 Powers
Powers come before minus and times.
Order: ( ) → x² √ → × ÷ → + −
(−2)³ means −2 times −2 times −2.
An odd number of minuses gives minus.
(−2)3 = (−2) × (−2) × (−2) = −8
That is −8.
= −8 − 2(−2)
3 Times and divide
Times comes before minus.
2(−2) = 2 × (−2)
+ × − = −
2(−2) means 2 times −2.
Plus times minus is minus.
2 times 2 is 4.
So we get −4.
= −8 − (−4)
4 Plus and minus
Taking away a negative is the same as adding.
− (−) = +
So −8 − (−4) becomes −8 + 4.
= −8 + 4
Start at −8.
Go up 4.
We land on −4.
f(−2) = −4
So f(−2) = −4.
Let's look back.
First: put the number in.
Then: powers.
Then: times and divide.
Last: plus and minus.
Answer
f(−2) = −4