First slide

Functions (XII)

Question

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

Easy

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

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

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