To find [tex]\( f(g(x)) \)[/tex], we'll substitute the function [tex]\( g(x) \)[/tex] into the function [tex]\( f(x) \)[/tex]. Let's work through the problem step-by-step:
1. Given Functions:
[tex]\[
f(x) = 8x
\][/tex]
[tex]\[
g(x) = x - 4
\][/tex]
2. Find [tex]\( f(g(x)) \)[/tex]:
This means we need to substitute [tex]\( g(x) \)[/tex] into [tex]\( f(x) \)[/tex].
3. Substitute [tex]\( g(x) = x - 4 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]\[
f(g(x)) = f(x - 4)
\][/tex]
4. Evaluate [tex]\( f(x - 4) \)[/tex]:
[tex]\[
f(x - 4) = 8(x - 4)
\][/tex]
5. Distribute the 8:
[tex]\[
8(x - 4) = 8x - 32
\][/tex]
Therefore, the composition of the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex], denoted [tex]\( f(g(x)) \)[/tex], is:
[tex]\[
f(g(x)) = 8x - 32
\][/tex]
So the final answer is:
[tex]\[
8x - 32
\][/tex]
