Let f(x)=lim(ntooo)(cos sqrt(x/n))^(n),g...

Let `f(x)=lim_(ntooo)(cos sqrt(x/n))^(n),g(x)=lim_(nto oo)(1+x+x root(n)(e))^(n)`
Now consider the function `y=h(x)` where `h(x)=tan^(-1)(g^(-1)f^(-1)(x))`.
Range of the function `y=h(x)` is

A

`(0,(pi)/2)`

B

`(-(pi)/2,0)`

C

`R`

D

`(-(pi)/2,(pi)/2)`

Verified by Experts

The correct Answer is:

D

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