Final answer:
The correct expression for (f g)(c) is D. (f - g)(c) = 6c - 322 + 48.
Step-by-step explanation:
To find (f g)(c), we need to evaluate the composite function (f g)(c) by substituting the expression for g(r) into the function f(c). Given that f(c) = 3 + 4 - 6 and g(r) = 6 - 52 - 2, we substitute g(r) into f(c) to obtain (f g)(c). This results in (f g)(c) = (3 + 4 - 6) - (6 - 52 - 2).
Now, simplify the expression inside the parentheses. For the first set, 3 + 4 - 6 becomes 1, and for the second set, -(6 - 52 - 2) simplifies to -(-56), which is equal to 56. Combining the results, (f g)(c) = 1 - 56, leading to (f g)(c) = -55.
Comparing this result with the options, the correct expression is D. (f - g)(c) = 6c - 322 + 48. Therefore, the answer is D. (f - g)(c) = 6c - 322 + 48.
In conclusion, by correctly substituting the expression for g(r) into f(c) and simplifying the resulting expression, we obtain the composite function (f g)(c), and by comparing it with the given options, we identify the correct expression.