Answer:
48x^2 - 48x + 38
Explanation:
To get the composite function first understand the process of which a function inside another operates.
First solve one step at a time by trying to evaluate the inside before evaluating the outside using substitution.
For instance, h(g(f(x))) is the h function of g function of f.
Since f(x) is the inner component of the composite function, replace the x of g with the value of f(x).
Such that g(x) = 3x^2 + 5 → 3(f(x))^2 + 5 →
3(2x - 1)^2 + 5 → 3(2x - 1)(2x - 1) + 5 [foil] → 3(4x^2 - 4x + 1) + 5 → 12x^2 - 12x + 3 + 5 →
12x^2 - 12x + 8
Thus g(f(x)) = 3(f(x))^2 + 5 = 12x^2 - 12x + 8.
Finally to compute h(g(f(x))), using the process from the first composite function, same can be applied here:
Since h(x) = 4x + 6 →
h(g(f(x))) =
h(12x^2 - 12x + 8) =
4(12x^2 - 12x + 8) + 6 [distribute] →
48x^2 - 48x + 32 + 6 [combine like terms] →
48x^2 - 48x + 38