If the function `f:[1,oo)->[1,oo)` is defined by `f(x)=2^(x(x-1)),` then `f^-1(x)` is (A) `(1/2)^(x(x-1))` (B) `1/2 sqrt(1+4log_2x)` (C) `1/2(1+sqrt(1+4log_2x))` (D) not defined

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

Explanation

To find the inverse of the function \( f(x) = 2^{x(x-1)} \), we will follow these steps:

### Step 1: Set up the equation
We start by letting \( y = f(x) \):
\[ y = 2^{x(x-1)} \]

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