Answer
$(f+g)(x)=x^2+5x+1$
$(f−g)(x)=x^2-5x+1$
$(f×g)(x)=5x^3+5x$
$(\frac{f}{g})(x)=\frac{x^2+1}{5x}$
Work Step by Step
If $f(x)=x^2+1$ and $g(x)=5x$, then
$(f+g)(x)=f(x)+g(x)=x^2+1+5x=x^2+5x+1$
$(f−g)(x)=f(x)−g(x)=x^2+1-5x=x^2-5x+1$
$(f×g)(x)=f(x)×g(x)=(x^2+1)×(5x)=5x^3+5x$
$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{x^2+1}{5x}$
