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Given [tex]f(x)=2x[/tex] and [tex]g(x)=x^2+3[/tex], find [tex]f(g(x))[/tex].

A. [tex]4x^2 + 3[/tex]
B. [tex]2x^2 + 3[/tex]
C. [tex]2x^2 + 6[/tex]
D. [tex]x^2 + 2x + 3[/tex]

Sagot :

GinnyAnswer
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]
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