Final answer:
To evaluate g(f(u)), we substitute u into f(x) to get f(u) = u²-4 and then substitute that result into g(x), resulting in g(f(u)) = (u²-4)³.
Step-by-step explanation:
To simplify or evaluate the function g(f(u)), we first need to determine what f(u) is. Given that f(x) = x²-4, we substitute u for x to get f(u) = u²-4. Now, we substitute f(u) into g(x), where g(x) = x³, so g(f(u)) becomes (u²-4)³.
This means that we are to compute the cube of the expression u²-4. To do so we multiply u²-4 by itself three times. The simplified result for the composition of the two functions is (u²-4)³, which is the value of g(f(u)).