Certainly! Let's solve the problem step by step.
We are given two functions:
[tex]\[ h(x) = x^2 + 1 \][/tex]
[tex]\[ k(x) = x - 2 \][/tex]
We need to find [tex]\((h + k)(2)\)[/tex].
### Step 1: Calculate [tex]\(h(2)\)[/tex]
To find [tex]\(h(2)\)[/tex], substitute [tex]\(x = 2\)[/tex] into the function [tex]\(h(x)\)[/tex]:
[tex]\[ h(2) = 2^2 + 1 \][/tex]
[tex]\[ h(2) = 4 + 1 \][/tex]
[tex]\[ h(2) = 5 \][/tex]
### Step 2: Calculate [tex]\(k(2)\)[/tex]
Next, substitute [tex]\(x = 2\)[/tex] into the function [tex]\(k(x)\)[/tex]:
[tex]\[ k(2) = 2 - 2 \][/tex]
[tex]\[ k(2) = 0 \][/tex]
### Step 3: Calculate [tex]\((h + k)(2)\)[/tex]
The function [tex]\((h + k)(x)\)[/tex] is defined as the sum of [tex]\(h(x)\)[/tex] and [tex]\(k(x)\)[/tex]:
[tex]\[ (h + k)(x) = h(x) + k(x) \][/tex]
So, when [tex]\(x = 2\)[/tex]:
[tex]\[ (h + k)(2) = h(2) + k(2) \][/tex]
[tex]\[ (h + k)(2) = 5 + 0 \][/tex]
[tex]\[ (h + k)(2) = 5 \][/tex]
Therefore, the value of [tex]\((h + k)(2)\)[/tex] is [tex]\(\boxed{5}\)[/tex].
