To solve for [tex]\( f(h+1) \)[/tex] given the function [tex]\( f(x) = 5x + 1 \)[/tex], follow these steps:
1. Identify the function and the input: The function we are given is [tex]\( f(x) = 5x + 1 \)[/tex]. We need to find [tex]\( f(h + 1) \)[/tex].
2. Substitute [tex]\( h+1 \)[/tex] into the function: Substitute [tex]\( h+1 \)[/tex] for [tex]\( x \)[/tex] in the given function. Thus, the function becomes:
[tex]\[
f(h+1) = 5(h+1) + 1
\][/tex]
3. Simplify the expression inside the function: Distribute the 5 inside the parentheses:
[tex]\[
f(h+1) = 5h + 5 \cdot 1 + 1 = 5h + 5 + 1
\][/tex]
4. Combine like terms: Combine the constants:
[tex]\[
f(h+1) = 5h + 6
\][/tex]
Given that [tex]\( h = 1 \)[/tex]:
5. Substitute [tex]\( h = 1 \)[/tex] into the simplified function:
[tex]\[
f(1+1) = 5 \cdot 1 + 6 = 5 + 6
\][/tex]
6. Calculate the final result:
[tex]\[
f(2) = 11
\][/tex]
Therefore, [tex]\( f(h+1) = 11 \)[/tex].
