Question

Given the definitions of f(x) and g(x) below, find the value of g(f(-3)).

f(x) = 4x + 8
g(x) = x2 + 2x + 7

Answer 1

To find the value of g(f(-3)), first calculate f(-3) which equals -4, then plug this value into g(x) to find that g(f(-3)) is 15.

Step-by-step explanation:

To find the value of g(f(-3)), first calculate the value of f(-3), then substitute that result into the function of g(x).

1. Start with f(x) = 4x + 8 and replace x with -3:
   f(-3) = 4(-3) + 8 which simplifies to f(-3) = -12 + 8 which is f(-3) = -4.
2. Next, take g(x) = x² + 2x + 7 and substitute f(-3) for x:
   g(f(-3)) = g(-4) = (-4)² + 2(-4) + 7.
3. Simplify g(-4) to get the result:
   g(-4) = 16 - 8 + 7 = 15.

Thus, the value of g(f(-3)) is 15.