If $f (x) = \sqrt{x}$ and $g (x) = x$ be two functions defined over the set of non-negative real numbers, Find $(f + g) (f g)$ and $(f / g)$ .

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Solution

given $f (x)$ = $x^{1 / 2}$ , $g (x) = x$

therefore $(f (x) + g (x)) (f (x) g (x)) = (x + x^{1 / 2}) (x^{3 / 2})$ = $x^{5 / 2} + x^{2}$

similarly $\frac{f (x)}{g (x)}$ = $x^{- 1 / 2}$

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