Step by step
The question
Question: find f(g(−2)) for f(x) = 4x − 3 and g(x) = x².
f(x) = 4x − 3
g(x) = x2
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.
We write it in brackets.
g(−2) = (−2)2
(−2)² means −2 times −2.
Minus times minus is plus.
(−2)2 = (−2) × (−2) = 4
That is 4.
g(−2) = 4
2 Then the outside
g(−2) is 4.
So f(g(−2)) is f(4).
f(g(−2)) = f(4)
Put 4 in place of x in f.
= 4(4) − 3
Times comes before minus.
Order: ( ) → x² √ → × ÷ → + −
4(4) = 4 × 4
4(4) means 4 times 4.
4 times 4 is 16.
= 16 − 3
16 minus 3 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