Alright, let's solve part (a) step-by-step.
We are given the function [tex]\( f(x) = 8x + 9 \)[/tex].
We need to find [tex]\( f(x + h) \)[/tex] and simplify.
1. Substitute [tex]\( x + h \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(x + h) = 8(x + h) + 9
\][/tex]
2. Distribute [tex]\( 8 \)[/tex] inside the parentheses:
[tex]\[
f(x + h) = 8x + 8h + 9
\][/tex]
So, the simplified form of [tex]\( f(x + h) \)[/tex] is:
[tex]\[
f(x + h) = 8x + 8h + 9
\][/tex]
