If the function `f:[1,oo)to[1,oo)` is defined by `f(x)=2^(x(x-1))` then `f^(-1)` is

Options

A. `((1)/(2))^(x(x-1))`
B. `(1)/(2)(1+sqrt(1+4log_(2)x))`
C. `(1)/(2)(1-sqrt(1-4log_(2)x))`
D. Not defined

Answer

B

Explanation

Given `f(x)=2^(x(x-1)) implies x(x-1) = log_2 f(x)`
`implies x^2 - x - log_2f(x)=0implies x= (1+-sqrt(4log_2f(x)))/2`
Only `f^-1(x)(1)/(2)(1+sqrt(1+4log_(2)x))`lies in the domain