Let's solve the given problem step-by-step:
1. We are given two functions:
[tex]\[
h(x) = x^2 + 1
\][/tex]
[tex]\[
k(x) = x - 2
\][/tex]
2. We need to evaluate [tex]\(h(2)\)[/tex] and [tex]\(k(2)\)[/tex].
3. Calculate [tex]\(h(2)\)[/tex]:
[tex]\[
h(2) = 2^2 + 1
\][/tex]
[tex]\[
h(2) = 4 + 1
\][/tex]
[tex]\[
h(2) = 5
\][/tex]
4. Calculate [tex]\(k(2)\)[/tex]:
[tex]\[
k(2) = 2 - 2
\][/tex]
[tex]\[
k(2) = 0
\][/tex]
5. To find [tex]\((h + k)(2)\)[/tex], we add the values of [tex]\(h(2)\)[/tex] and [tex]\(k(2)\)[/tex]:
[tex]\[
(h + k)(2) = h(2) + k(2)
\][/tex]
[tex]\[
(h + k)(2) = 5 + 0
\][/tex]
[tex]\[
(h + k)(2) = 5
\][/tex]
Therefore:
[tex]\[
(h + k)(2) = \boxed{5}
\][/tex]
