Please help Algebra 2 CC Function Question!

Question

Given f(x)=x^2 and g(x)=x-3, express g(f(x+2)) as a polynomial in simplest form.

Answer 1

First, we must solve for f(x+2). When x is x+2, then f(x+2)=(x+2)²--->x²+4x+4. Now, when x in the function g(x)=x-3 is x²+4x+4 we get g(x²+4x+4)=(x²+4x+4)-3--->x²+4x+1. Therefore, the answer is x²+4x+1.

Answer 2

f(x) = x²

g(x) = x - 3

To find f(x+2), just replace the x with x+2:

f(x+2) = (x+2)² = x² + 4x + 4

To find g(f(x+2)), just replace the x in g(x) with f(x+2):

g(f(x+2)) = f(x+2) - 3 = x² + 4x + 4 - 3 = ______?