Step by step
The question
Question: find f(g(2)) for f(x) = x² − 3 and g(x) = 2x + 1.
f(x) = x2 − 3
g(x) = 2x + 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.
We write it in brackets: 2x becomes 2 times 2, not 22.
g(2) = 2(2) + 1
Everyone uses the same order, so we all get the same answer.
Times comes before plus.
2(2) means 2 times 2.
Order: × ÷ → + −
2(2) = 2 × 2
2 times 2 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.
= 52 − 3
Everyone uses the same order, so we all get the same answer.
Powers come before minus.
Order: Powers → + −
5² means 5 times 5.
52 = 5 × 5 = 25
That is 25.
= 25 − 3
25 minus 3 is 22.
f(g(2)) = 22
So f(g(2)) = 22.
3 Type it in
The answer box takes 5 characters.
22 has 2.
It fits.
22: 2 characters, up to 5 fit
We type 22.
Let's look back.
First: work out the inside.
Then: then the outside.
Last: type it in.
Answer
f(g(2)) = 22