To find [tex]\((h + k)(2)\)[/tex], we'll go through the following steps:
1. Evaluate [tex]\( h(x) \)[/tex] at [tex]\( x = 2 \)[/tex]:
First, we need to find [tex]\( h(2) \)[/tex]. The function [tex]\( h(x) \)[/tex] is given by:
[tex]\[
h(x) = x^2 + 1
\][/tex]
Substituting [tex]\( x = 2 \)[/tex] into the function,
[tex]\[
h(2) = 2^2 + 1 = 4 + 1 = 5
\][/tex]
2. Evaluate [tex]\( k(x) \)[/tex] at [tex]\( x = 2 \)[/tex]:
Next, we need to find [tex]\( k(2) \)[/tex]. The function [tex]\( k(x) \)[/tex] is given by:
[tex]\[
k(x) = x - 2
\][/tex]
Substituting [tex]\( x = 2 \)[/tex] into the function,
[tex]\[
k(2) = 2 - 2 = 0
\][/tex]
3. Calculate [tex]\((h + k)(2)\)[/tex]:
The next step is to add the values of [tex]\( h(2) \)[/tex] and [tex]\( k(2) \)[/tex] to find [tex]\((h + k)(2)\)[/tex]:
[tex]\[
(h + k)(2) = h(2) + k(2)
\][/tex]
Substituting the values we found,
[tex]\[
(h + k)(2) = 5 + 0 = 5
\][/tex]
So, [tex]\((h + k)(2) = 5\)[/tex].
