To find [tex]\( f(g(x)) \)[/tex], we need to first understand what each function does:
1. [tex]\( f(x) = 2x \)[/tex]
2. [tex]\( g(x) = x^2 + 3 \)[/tex]
We start by finding [tex]\( g(x) \)[/tex] for a general [tex]\( x \)[/tex]:
[tex]\[ g(x) = x^2 + 3 \][/tex]
Next, we substitute [tex]\( g(x) \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]\[ f(g(x)) = f(x^2 + 3) \][/tex]
Given [tex]\( f(x) = 2x \)[/tex], we replace [tex]\( x \)[/tex] with [tex]\( x^2 + 3 \)[/tex]:
[tex]\[ f(g(x)) = 2(x^2 + 3) \][/tex]
We then distribute the 2 across the terms inside the parentheses:
[tex]\[ f(g(x)) = 2x^2 + 6 \][/tex]
Thus, the expression [tex]\( f(g(x)) \)[/tex] simplifies to:
[tex]\[ f(g(x)) = 2x^2 + 6 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{2x^2 + 6} \][/tex]
