Alright, let's find the expression for [tex]\((f + g)(x)\)[/tex] step-by-step.
Given:
[tex]\( f(x) = x^2 + 1 \)[/tex]
[tex]\( g(x) = 5 - x \)[/tex]
We need to find [tex]\((f + g)(x)\)[/tex].
1. [tex]\((f + g)(x)\)[/tex] represents the sum of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
(f + g)(x) = f(x) + g(x)
\][/tex]
2. Substitute [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into the equation:
[tex]\[
(f + g)(x) = (x^2 + 1) + (5 - x)
\][/tex]
3. Combine like terms:
[tex]\[
(f + g)(x) = x^2 + 1 + 5 - x
\][/tex]
4. Simplify the expression by combining the constants and like terms:
[tex]\[
(f + g)(x) = x^2 - x + 6
\][/tex]
So, [tex]\((f + g)(x)\)[/tex] is [tex]\(x^2 - x + 6\)[/tex].
From the given choices, the correct answer is:
[tex]\(x^2 - x + 6\)[/tex].
