Final answer:
The composition of two functions g(f(c)) was calculated, and after simplifying the expression, the result was found to be -7.5 + 36c, which does not align with any of the given answer options, suggesting an issue within the question itself. The correct option is c.
Step-by-step explanation:
The student is asking for the value of the function g(f(c)), which requires composing the function g(t) with the function f(x). First, we substitute f(x) into g(t) to get g(f(x)). Since f(x) = 1/2 + 4x and g(t) = 9t – 12, when we input f(c) into g(t), we write it as g(f(c)) = 9(1/2 + 4c) – 12. Simplifying this expression, we have:
- Multiply 9 with both terms inside the parenthesis: 9 * 1/2 and 9 * 4c.
- Add the results together with – 12 to find the simplified form.
The actual steps of the calculation show that g(f(c)) = 9/2 + 36c – 12, which simplifies further to g(f(c)) = 4.5 + 36c – 12. Subtracting 12 from 4.5 gives us – 7.5 + 36c. This result does not match any of the provided options, which indicates there might be an error in the options given or in the original functions provided. The correct option is c.