Final answer:
After composing f(-6) and g(f(-6)), we find that g(f(-6)) equals -10; however, this answer is not listed in the provided options, implying an error in the question or its options.
Step-by-step explanation:
To find g(f(-6)), we first need to find the value of f(-6). The function f(x) = 5x + 2 is given, so we substitute x with -6:
f(-6) = 5(-6) + 2 = -30 + 2 = -28
Now we have the value of f(-6), and we can substitute this value into the function g(x), where g(x) = 1/2x + 4:
g(f(-6)) = g(-28) = 1/2(-28) + 4 = -14 + 4 = -10
However, none of the given options match -10, so either there is an error in the provided options or in the calculation of g(f(-6)).
Considering that it is important to provide a factually accurate response, please review the options or the question to ensure they are correctly given.