To find g(h(x)), we need to substitute the function h(x) into the function g(x). Let's go step-by-step:
1. Start with the function g(x) = 4x - 1.
2. Substitute h(x) into g(x) by replacing x in g(x) with h(x).
g(h(x)) = 4h(x) - 1.
3. Replace h(x) with its definition, which is 3x + 3.
g(h(x)) = 4(3x + 3) - 1.
4. Simplify the expression inside the parentheses by multiplying:
g(h(x)) = 12x + 12 - 1.
5. Combine like terms:
g(h(x)) = 12x + 11.
Therefore, g(h(x)) = 12x + 11.
This means that the composite function g(h(x)) takes the input x,
applies the function h(x) = 3x + 3, and
then applies the function g(x) = 4x - 1
to the result.