Question

Let $f:[0,\infty ]\to R$ and $g:R\to R$ be defined by $f\left(x\right)=\sqrt{x}$ and g(x) = x. Find f + g, f - g, fg and $\frac{f}{g}$

Answer 1

$f+g:[0,\infty )\to R$ defined by $(f+g)\left(x\right)=\sqrt{x}+x$;
$f-g:[0,\infty )\to R$ defined by $(f-g)\left(x\right)=\sqrt{x}+x$;
$fg:[0,\infty )\to R$ defined by $\left(fg\right)\left(x\right)=x^{\frac{3}{2}}$
$\frac{f}{g}:[0,\infty )\to R$ defined by $\left(\frac{f}{g}\right)\left(x\right)=\frac{1}{\sqrt{x}}$