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

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

C)  \[\frac{1}{2}(1-\sqrt{1+4{{\log }_{2}}x})\]

D)  Not defined