Final answer:
To find f(g(x)), the function g(x) = 3x^2 - 7 is substituted into f(x), resulting in f(g(x)) = 4|3x^2 - 9| + 3, which is the composition of the two functions.
Step-by-step explanation:
To find f(g(x)), we need to compose the functions f(x) and g(x). That means we'll substitute g(x) into f(x).
First, we have g(x) = 3x^2 - 7. To find f(g(x)), we need to evaluate f(3x^2 - 7).
The function f(x) = 4|x - 2| + 3 becomes f(3x^2 - 7) = 4|3x^2 - 7 - 2| + 3, which simplifies to:
f(3x^2 - 7) = 4|3x^2 - 9| + 3
This expression cannot be further simplified without knowing the value of x. Hence, the composition f(g(x)) is 4|3x^2 - 9| + 3.