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  4. If f(x) = (x/√1 -x2) ,then (fof) (x) =

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Q. If $f(x) = \frac{x}{\sqrt{1 -x^2}}$ ,then $(fof) (x) = $

Relations and Functions - Part 2

Solution:

$fof(x) = f(f(x)) = \frac{f(x)}{\sqrt{1 - (f(x))^2}}$
$= \frac{x\sqrt{1 - x^{2}} }{\sqrt{1 - \frac{x^{2}}{1 - x^{2}}}} =\frac{x}{\sqrt{1 - 2x^{2}}}$