To solve this problem, we first need to define the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ f(x) = x^2 + 1 \][/tex]
[tex]\[ g(x) = 5 - x \][/tex]
Next, we need to find the value of [tex]\((f + g)(x)\)[/tex], which is the sum of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
Substituting the given functions into this expression:
[tex]\[ (f + g)(x) = (x^2 + 1) + (5 - x) \][/tex]
Now, let's combine the like terms:
[tex]\[ (f + g)(x) = x^2 + 1 + 5 - x \][/tex]
[tex]\[ (f + g)(x) = x^2 - x + 6 \][/tex]
Therefore, the simplified expression for [tex]\((f + g)(x)\)[/tex] is:
[tex]\[ \boxed{x^2 - x + 6} \][/tex]
So, the correct answer from the given options is:
[tex]\[ x^2 - x + 6 \][/tex]
