Step by step
The question
Question: find f(g(3)) for f(x) = 2x + 1 and g(x) = x².
f(x) = 2x + 1
g(x) = x2
1 Work out the inside
f(g(3)) is a function inside a function.
Like with brackets, we start inside.
f works on what g(3) gives.
So first g(3).
inside first: g(3)
3 → g → f
Put 3 in place of x in g.
g(3) = 32
3² means 3 times 3.
32 = 3 × 3 = 9
That is 9.
g(3) = 9
2 Then the outside
g(3) is 9.
So f(g(3)) is f(9).
f(g(3)) = f(9)
Put 9 in place of x in f.
= 2(9) + 1
Everyone uses the same order, so we all get the same answer.
Times comes before plus.
2(9) means 2 times 9.
Order: × ÷ → + −
2(9) = 2 × 9
2 times 9 is 18.
= 18 + 1
18 plus 1 is 19.
f(g(3)) = 19
So f(g(3)) = 19.
3 Type it in
The answer box takes 5 characters.
19 has 2.
It fits.
19: 2 characters, up to 5 fit
We type 19.
Let's look back.
First: work out the inside.
Then: then the outside.
Last: type it in.
Answer
f(g(3)) = 19