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If f(x)=cot^-1 x ; R^+ -> (0,pi/2) and...

If `f(x)=cot^-1 x ; R^+ -> (0,pi/2) and g(x)=2x-x^2 ; R-> R` . Then the range of the function `f(g(x)) ` where verdefined is

A

`(0,(pi)/2)`

B

`(0,(pi)/4)`

C

`[(pi)/4,(pi)/2)`

D

`{(pi)/4}`

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The correct Answer is:
C
NA
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