Step by step
The question
Question: find f(f(2)) for f(x) = 3x − 1.
f(x) = 3x − 1
1 Work out the inside
f(f(2)) is a function inside a function.
Like with brackets, we start inside.
First f(2).
inside first: f(2)
Put 2 in place of x in f.
We write it in brackets.
f(2) = 3(2) − 1
Times comes before minus.
Order: ( ) → x² √ → × ÷ → + −
3(2) = 3 × 2
3(2) means 3 times 2.
3 times 2 is 6.
= 6 − 1
6 minus 1 is 5.
f(2) = 5
2 Then the outside
f(2) is 5.
So f(f(2)) is f(5).
f(f(2)) = f(5)
Put 5 in place of x in f.
= 3(5) − 1
Times comes before minus.
Order: ( ) → x² √ → × ÷ → + −
3(5) = 3 × 5
3(5) means 3 times 5.
3 times 5 is 15.
= 15 − 1
15 minus 1 is 14.
f(f(2)) = 14
So f(f(2)) = 14.
Let's look back.
First: work out the inside.
Last: then the outside.
Answer
f(f(2)) = 14