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If the function f : [1, oo) rarr [1, oo)...

If the function `f : [1, oo) rarr [1, oo)` is defined by `f(x) = 2^(x(x - 1))`, then `f^(-1) (x)` is a)`((1)/(2))^(x(x-1))` b)`(1)/(2) (1 - sqrt(1 + 4 log_(2)x))` c)`(1)/(2) sqrt(1 + 4 log_(2)x)` d)`(1)/(2) [1 + sqrt(1 + 4 log_(2)x)]`

A

`((1)/(2))^(x(x-1))`

B

`(1)/(2) (1 - sqrt(1 + 4 log_(2)x))`

C

`(1)/(2) sqrt(1 + 4 log_(2)x)`

D

`(1)/(2) [1 + sqrt(1 + 4 log_(2)x)]`

Text Solution

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The correct Answer is:
D
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