Final answer:
To compute g(h(x)), substitute h(x) into g(x), which results in a composition that is not listed in the given options, making option (d) the correct answer.
Step-by-step explanation:
The question asks for the composition of two functions, which means we need to find g(h(x)). Here, g(x) = 3x² + 2 and h(x) = 2x + 2. To find g(h(x)), we substitute h(x) into every occurrence of x in g(x).
First, calculate h(x): h(x) = 2x + 2.
Now, substitute h(x) into g(x): g(h(x)) = 3(2x + 2)² + 2. Next, expand (2x + 2)²: (2x + 2)² = 4x² + 8x + 4.
Substitute this back into the g(x) equation: g(h(x)) = 3(4x² + 8x + 4) + 2 = 12x² + 24x + 12 + 2 = 12x² + 24x + 14.
The correct answer is not listed in the options provided by the student, which means the choice is (d) There is no correct answer given.