Question

f(x)=x²+1 g(x)=5−x
(f+g)(x)=
○ x²+x−4
○ x²+x+4
○ x²−x+6
○ x²+x+6

Explanation:

Step1: Recall the definition of function addition

To find \((f + g)(x)\), we use the definition \((f + g)(x)=f(x)+g(x)\).

Step2: Substitute the given functions

We know that \(f(x)=x^{2}+1\) and \(g(x) = 5 - x\). So we substitute these into the formula:
\((f + g)(x)=(x^{2}+1)+(5 - x)\)

Step3: Simplify the expression

Remove the parentheses and combine like terms:
\(x^{2}+1 + 5-x=x^{2}-x+(1 + 5)=x^{2}-x + 6\)

Answer:

\(x^{2}-x + 6\) (corresponding to the option \(x^{2}-x + 6\))