Final answer:
To evaluate g(2) and f(g(2)), first g(2) is calculated by substituting x with 2 in g(x) resulting in 0. Then, f(g(2)) is evaluated by substituting this result into f(x), leading to a final result of -4.
Step-by-step explanation:
The student is asking to evaluate two expressions involving functions: first, the value of the function g at 2, which is g(2), and then the value of the function f at g(2), which is f(g(2)).
Starting with g(2), we substitute x with 2 in the function g(x) = -2x + 4. Thus, g(2) = -2(2) + 4 = -4 + 4 = 0.
Moving on to f(g(2)), we have f(0) since g(2) = 0. Now we evaluate the function f(x) = x² - x - 4 at x = 0. That gives us f(0) = (0)² - (0) - 4 = -4.
To evaluate g(2), we substitute 2 into the function g(x) = -2x + 4:
g(2) = -2(2) + 4 = 0
So, g(2) = 0.
To evaluate f(g(2)), we substitute g(2) into the function f(x) = x² - x - 4:
f(g(2)) = f(0) = (0)² - (0) - 4 = -4
Therefore, f(g(2)) = -4.