1) The domain of the function f(x) = $\sqrt{\frac{1}{|x-2|-(x-2)}}$ is: A) $(-\infty,2)$ B) $(2,\infty)$ C) $(-\infty,2)$ D) $(2,\infty)$ Answer: Option CExplanation:|x-2| = $\begin{cases}x-2 & x \geq 2\\2-x & x < 2\end{cases}$ |x-2|-(x-2) = $\begin{cases}0 & x \geq 2\\4-2x & x < 2\end{cases}$ given expression is defined for (-∞ ,2)
