Step by step
The question
Question: find f(g(2)) for f(x) = 3x − 2 and g(x) = x² + 1.
f(x) = 3x − 2
g(x) = x2 + 1
1 Work out the inside
f(g(2)) is a function inside a function.
Like with brackets, we start inside.
f works on what g(2) gives.
So first g(2).
inside first: g(2)
2 → g → f
Put 2 in place of x in g.
g(2) = 22 + 1
Everyone uses the same order, so we all get the same answer.
Powers come before plus.
Order: Powers → + −
2² means 2 times 2.
22 = 2 × 2
= 4
That is 4.
= 4 + 1
4 plus 1 is 5.
g(2) = 5
2 Then the outside
g(2) is 5.
So f(g(2)) is f(5).
f(g(2)) = f(5)
Put 5 in place of x in f.
= 3(5) − 2
Everyone uses the same order, so we all get the same answer.
Times comes before minus.
3(5) means 3 times 5.
Order: × ÷ → + −
3(5) = 3 × 5
3 times 5 is 15.
= 15 − 2
15 minus 2 is 13.
f(g(2)) = 13
So f(g(2)) = 13.
Let's look back.
First: work out the inside.
Last: then the outside.
Answer
f(g(2)) = 13