express your answer as a polynomial in standard form.\n$f(x) = x - 4$\n$g(x) = 3x^2 + 6x + 9$\nfind: $(f…

express your answer as a polynomial in standard form.\n$f(x) = x - 4$\n$g(x) = 3x^2 + 6x + 9$\nfind: $(f \\circ g)(x)$

express your answer as a polynomial in standard form.\n$f(x) = x - 4$\n$g(x) = 3x^2 + 6x + 9$\nfind: $(f \\circ g)(x)$

Answer

Explanation:

Step1: Recall composition of functions

The composition ((f \circ g)(x)) means (f(g(x))). So we substitute (g(x)) into (f(x)).

Step2: Substitute (g(x)) into (f(x))

Given (f(x)=x - 4) and (g(x)=3x^{2}+6x + 9), then (f(g(x))=f(3x^{2}+6x + 9)). Substitute (3x^{2}+6x + 9) for (x) in (f(x)): (f(3x^{2}+6x + 9)=(3x^{2}+6x + 9)-4).

Step3: Simplify the expression

Simplify ((3x^{2}+6x + 9)-4) by combining like terms: (3x^{2}+6x+(9 - 4)=3x^{2}+6x + 5).

Answer:

(3x^{2}+6x + 5)