If f(y)=y1-y2,g(y)=y1+y2,then (fog)(y) is equal to

A
$\frac{y}{\sqrt{(1 - y^{2})}}$
B
$\frac{y}{\sqrt{(1 + y^{2})}}$
C
y
D
$\frac{(1 - y^{2})}{\sqrt{(1 - y^{2})}}$

Solution:

$f (y) = \frac{y}{\sqrt{(1 - y^{2})}}, g (y) = \frac{y}{\sqrt{(1 + y^{2})}} and (fog) y = f (g (y)) = f (\frac{y}{\sqrt{(1 + y^{2})}}) = \frac{\frac{y}{\sqrt{(1 + y^{2})}}}{\sqrt{1 - \frac{y^{2}}{(1 + y^{2})}}} = \frac{\frac{y}{\sqrt{(1 + y^{2})}}}{\frac{1}{\sqrt{(1 + y^{2})}}} = y$

If $f (y) = \frac{y}{\sqrt{(1 - y^{2})}}, g (y) = \frac{y}{\sqrt{(1 + y^{2})}},$ then (fog)(y) is equal to

Solution:

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