To find [tex]\((f + g)(x)\)[/tex] given the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], we need to add the two functions together.
Given:
[tex]\[ f(x) = x^2 + 1 \][/tex]
[tex]\[ g(x) = 5 - x \][/tex]
The combined function [tex]\( (f + g)(x) \)[/tex] is defined as:
[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f + g)(x) = (x^2 + 1) + (5 - x) \][/tex]
Now, combine the terms:
[tex]\[ (f + g)(x) = x^2 + 1 + 5 - x \][/tex]
[tex]\[ (f + g)(x) = x^2 - x + 6 \][/tex]
Thus, the combined function is:
[tex]\[ (f + g)(x) = x^2 - x + 6 \][/tex]
Therefore, the correct answer is:
[tex]\[ x^2 - x + 6 \][/tex]
