Write Expressions: To find the sum of the functions f(x) and g(x), we need to add the two functions together. The function f(x) is given as f(x)=x2+1, and the function g(x) is given as g(x)=5−x. We will add these two functions to find (f+g)(x).
Add Functions: We write down the expressions for f(x) and g(x) next to each other to prepare for addition: f(x)=x2+1 and g(x)=5−x.
Combine Like Terms: Now we add the two functions together: (f+g)(x)=f(x)+g(x)=(x2+1)+(5−x).
Simplify Constants: We combine like terms in the expression: (f+g)(x)=x2+1+5−x.
Simplify Constants: We combine like terms in the expression: (f+g)(x)=x2+1+5−x.Simplify the constant terms: (f+g)(x)=x2−x+6.