Sure, let’s solve this step-by-step.
We are given two functions:
[tex]\[ f(x) = 2x + 1 \][/tex]
[tex]\[ g(x) = x^2 \][/tex]
To find the value of [tex]\( f(g(3)) \)[/tex], we need to follow these steps:
1. Calculate [tex]\( g(3) \)[/tex]:
[tex]\[ g(x) = x^2 \][/tex]
So,
[tex]\[ g(3) = 3^2 = 9 \][/tex]
2. Now, we need to find [tex]\( f(g(3)) \)[/tex]. We substitute [tex]\( g(3) \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = 2x + 1 \][/tex]
Substitute [tex]\( x = g(3) = 9 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]\[ f(9) = 2 \cdot 9 + 1 = 18 + 1 = 19 \][/tex]
Thus,
[tex]\[ f(g(3)) = 19 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{19} \][/tex]
