Answer
$(f+g)(x)=x^2+x+3$
$(fg)(x)=x^3+2x^2+x+2$
Work Step by Step
We are given the functions:
$f(x)=x^2+1$
$g(x)=x+2$
The domains and ranges of $f$ and $g$ are the set of real, numbers, therefore $f+g$ and $fg$ have the same domain and range.
Compute $(f+g)(x)$:
$(f+g)(x)=f(x)+g(x)=x^2+1+x+2=x^2+x+3$
Compute $(fg)(x)$:
$(fg)(x)=f(x)g(x)=(x^2+1)(x+2)=x^3+2x^2+x+2$
