To solve for [tex]\((h+k)(2)\)[/tex], follow these steps:
1. Calculate [tex]\(h(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
- Given [tex]\(h(x) = x^2 + 1\)[/tex], substitute [tex]\(x = 2\)[/tex]:
[tex]\[
h(2) = 2^2 + 1 = 4 + 1 = 5
\][/tex]
2. Calculate [tex]\(k(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
- Given [tex]\(k(x) = x - 2\)[/tex], substitute [tex]\(x = 2\)[/tex]:
[tex]\[
k(2) = 2 - 2 = 0
\][/tex]
3. Combine [tex]\(h(2)\)[/tex] and [tex]\(k(2)\)[/tex] to find [tex]\((h + k)(2)\)[/tex]:
- [tex]\((h + k)(2)\)[/tex] means adding the values of [tex]\(h(2)\)[/tex] and [tex]\(k(2)\)[/tex]:
[tex]\[
(h + k)(2) = h(2) + k(2) = 5 + 0 = 5
\][/tex]
Therefore, the value of [tex]\((h+k)(2)\)[/tex] is:
[tex]\[
(h+k)(2) = 5
\][/tex]
