Let f :[2,oo)to {1,oo) defined by f (x)=...

Let `f :[2,oo)to {1,oo)` defined by `f (x)=2^(x ^(4)-4x ^(3))and g : [(pi)/(2), pi] to A ` defined by `g (x) = (sin x+4)/(sin x-2)` be two invertible functions, then
` f ^(-1) (x)` is equal to

A

`sqrt(2+sqrt(4-log_(2)x))`

B

`sqrt(2+sqrt(4+log_(2)x))`

C

`sqrt(2-sqrt(4+log_(2)x))`

D

None of these

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The correct Answer is:

b

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Let `f :[2,oo)to {1,oo)` defined by `f (x)=2^(x ^(4)-4x ^(3))and g : [(pi)/(2), pi] to A ` defined by `g (x) = (sin x+4)/(sin x-2)` be two invertible functions, then ` f ^(-1) (x)` is equal to

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Let `f :[2,oo)to {1,oo)` defined by `f (x)=2^(x ^(4)-4x ^(3))and g : [(pi)/(2), pi] to A ` defined by `g (x) = (sin x+4)/(sin x-2)` be two invertible functions, then
` f ^(-1) (x)` is equal to