if (f(x)=3x + 2) and (g(x)=x^{2}+1), which expression is equivalent to ((fcirc g)(x))?\n((3x +…

if (f(x)=3x + 2) and (g(x)=x^{2}+1), which expression is equivalent to ((fcirc g)(x))?\n((3x + 2)(x^{2}+1)\n3x^{2}+1 + 2\n(3x + 2)^{2}+1\n3(x^{2}+1)+2)

if (f(x)=3x + 2) and (g(x)=x^{2}+1), which expression is equivalent to ((fcirc g)(x))?\n((3x + 2)(x^{2}+1)\n3x^{2}+1 + 2\n(3x + 2)^{2}+1\n3(x^{2}+1)+2)

Answer

Explanation:

Step1: Recall composition - function definition

The composition ((f\circ g)(x)=f(g(x))).

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

Given (f(x) = 3x+2) and (g(x)=x^{2}+1), we substitute (x) in (f(x)) with (g(x)). So (f(g(x))=3(g(x)) + 2).

Step3: Replace (g(x)) with its expression

Since (g(x)=x^{2}+1), then (f(g(x))=3(x^{2}+1)+2).

Answer:

D. (3(x^{2}+1)+2)