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