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If f(y) = (y)/(sqrt(1-y^(2))), g(y) = (y...

If `f(y) = (y)/(sqrt(1-y^(2))), g(y) = (y)/(sqrt(1+y^(2)))`, then (fog) y is equal to

A

`(y)/(sqrt(1-y^(2)))`

B

`(y)/(sqrt(1+y^(2)))`

C

y

D

`((1-y^(2)))/(sqrt(1-y^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(y)=(y)/(sqrt((1-y^(2)))),g(y)=(y)/(sqrt((1+y^(2))))`
and `(fog)y=f(g(y))=f((y)/(sqrt((1+y^(2)))))=((y)/(sqrt((1+y^(2)))))/(sqrt(1-(y^(2))/((1+y^(2)))))=((y)/(sqrt((1+y^(2)))))/((1)/(sqrt((1+y^(2)))))=y`
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