Question

If $f : [1, \infty) \to [1, \infty)$ is defined by $f(x) = 2^{x(x-1)}$, then $f^{-1}(x) =$

• A. $\frac{1}{2} [1 + \sqrt{1 + 4 \log_2 x}]$
• B. $\frac{1}{2} [1 - \sqrt{1 + 4 \log_2 x}]$
• C. $\frac{1}{2} [1 + \sqrt{1 - 4 \log_2 x}]$
• D. $\frac{1}{2} [1 - \sqrt{1 - 4 \log_2 x}]$

Hint:

Since the domain is $x \ge 1$, the inverse function must also return a value $\ge 1$ for any $x \ge 1$. The negative branch yields values $\le 0.5$, which immediately rules it out.

Answer 1

The Correct Option is A