If $A=\{x:x\in R\:and\:x\geq 1\}$ and $f:A\rightarrow A$ is defined as $f(x)=2^{x(x-1)},$ then find $f^{-1}(x).$

Question

(A) $\large\frac{1+\sqrt{1+4log_2x}}{2}$

(B) $\large\big(\frac{1}{2}\big)^{x(x-1)}$

(C) $\large\frac{1-\sqrt{1+4log_2x}}{2}$

(D) none of these