Final answer:
To find f(g(-3)), evaluate g(-3) and substitute into f(x). To find g(f(-3)), evaluate f(-3) and substitute into g(x).
Step-by-step explanation:
To find f(g(-3)), we need to first evaluate g(-3) and then substitute that value into f(x).
Given that g(x) = 2 - x^2, we can substitute -3 into x to find g(-3):
g(-3) = 2 - (-3)^2 = 2 - 9 = -7
Now, we can substitute -7 into f(x) to find f(g(-3)):
f(g(-3)) = f(-7) = 4(-7) - 1 = -28 - 1 = -29
To find g(f(-3)), we need to first evaluate f(-3) and then substitute that value into g(x).
Given that f(x) = 4x - 1, we can substitute -3 into x to find f(-3):
f(-3) = 4(-3) - 1 = -12 - 1 = -13
Now, we can substitute -13 into g(x) to find g(f(-3)):
g(f(-3)) = g(-13) = 2 - (-13)^2 = 2 - 169 = -167
The student is asking to evaluate two composite functions, f(g(x)) and g(f(x)). First, we need to substitute g(x) into function f to find f(g(‑3)) and then substitute f(x) into function g to find g(f(‑3)).
Calculate g(‑3): g(‑3) = 2 – (‑3)² = 2 – 9 = ‑7.
Calculate f(g(‑3)): f(g(‑3)) = f(‑7) = 4(‑7) – 1 = ‑28 – 1 = ‑29.
Calculate f(‑3): f(‑3) = 4(‑3) – 1 = ‑12 – 1 = ‑13.
Calculate g(f(‑3)): g(f(‑3)) = g(‑13) = 2 – (‑13)² = 2 – 169 = ‑167.