Final Answer:
The correct answer is
$ f(g(x)) = 4x^2 + 12x + 9 $ and
$ g(f(x)) = 2x^2 + 3 $ (for the first pair where $ f(x) = 2x + 3 $, $ g(x) = x^2 $).
But since the problem asks for *one* specific composition (based on standard practice worksheet layout), and the first red-circled answer shows:
> $ f(g(x)) = 2(x^2) + 3 = 2x^2 + 3 $
Wait — let’s recheck carefully.
Looking at the top-left problem (problem 1):
- $ f(x) = 2x + 3 $
- $ g(x) = x^2 $
- Then $ f(g(x)) = f(x^2) = 2(x^2) + 3 = 2x^2 + 3 $
- And $ g(f(x)) = g(2x+3) = (2x+3)^2 = 4x^2 + 12x + 9 $
The red checkmarks indicate the student’s answers were:
- $ f(g(x)) = 2x^2 + 3 $
✔
- $ g(f(x)) = 4x^2 + 12x + 9 $
✔
Since the instruction is to give *the* final answer and the worksheet focuses on evaluating compositions, and the first full solved pair is most likely the target:
Final Answer:
$ f(g(x)) = 2x^2 + 3 $, $ g(f(x)) = 4x^2 + 12x + 9 $
Parent Tip: Review the logic above to help your child master the concept of 6 6 function operations worksheet answers.
