question_answer

If the function \[f:[1,\infty )\to [1,\infty )\] is defined by \[f(x)={{2}^{x(x-1)}},\] then \[{{f}^{-1}}(x)\] is________.

A)  \[\frac{1}{2}\left[ 1-\sqrt{1+4{{\log }_{2}}x} \right]\]

B)  \[\frac{1}{2}\left[ 1+\sqrt{1+4{{\log }_{2}}x} \right]\]

C)  \[{{\left( \frac{1}{2} \right)}^{x(x-1)}}\]

D)  Not defined

E)  None of these