If $f (x) = x^{2}$ and $g (x) = 2 x + 1$ be two real valued function. Find $(f g) (x)$ and $(\frac{f}{g}) (x) .$

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Solution

$f (x) = x^{2}$

$f (g (x)) = f (2 x + 1) = {(2 x + 1)}^{2}$

$∴ f (g (x)) = 4 x^{2} + 4 x + 1$

$\frac{f}{g} (x) = \frac{f (x)}{g (x)} = \frac{x^{2}}{2 x + 1}$

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