To find [tex]\( f(g(x)) \)[/tex] given the functions [tex]\( f(x) = 2x + 5 \)[/tex] and [tex]\( g(x) = 4x - 2 \)[/tex], follow these steps:
1. Calculate [tex]\( g(x) \)[/tex] :
[tex]\[
g(x) = 4x - 2
\][/tex]
2. Substitute [tex]\( g(x) \)[/tex] into [tex]\( f(x) \)[/tex] to find [tex]\( f(g(x)) \)[/tex] :
[tex]\[
f(g(x)) = f(4x - 2)
\][/tex]
3. Substitute [tex]\( 4x - 2 \)[/tex] into the function [tex]\( f(x) \)[/tex] :
[tex]\[
f(4x - 2) = 2(4x - 2) + 5
\][/tex]
4. Simplify the expression:
[tex]\[
2(4x - 2) + 5 = 2 \cdot 4x + 2 \cdot (-2) + 5
\][/tex]
[tex]\[
= 8x - 4 + 5
\][/tex]
[tex]\[
= 8x + 1
\][/tex]
So, the result of [tex]\( f(g(x)) \)[/tex] is [tex]\( 8x + 1 \)[/tex].
Therefore, among the given options:
- [tex]\( 8x - 9 \)[/tex]
- [tex]\( 8x + 9 \)[/tex]
- [tex]\( 8x - 1 \)[/tex]
- [tex]\( 8x + 1 \)[/tex]
The correct answer is [tex]\( 8x + 1 \)[/tex].
