# The domain of $f(x)=\left(\Bigl\lvert\bigl\lfloor |x|-1\bigr\rfloor\Bigr\rvert-5\right)^{-1/2}$

How should I find the domain of the following function?

$$f(x)=\left(\Bigl\lvert\bigl\lfloor |x|-1\bigr\rfloor\Bigr\rvert-5\right)^{-1/2}$$

I am getting something like $6\leq|x|<7$ but not sure whether I'm right. What will be the best approach?

You have tried to find the domain, which is the possible $x$-values. The range is the possible $y$-values.
The function inside the absolute value signs can be any integer greater than or equal to $-1$. So the possible values for $f(x)$ is a list of numbers, one value each for most of those integers.
• $\lfloor| x|\rfloor-1>5$ or $\lfloor |x|\rfloor-1<-5$. The second case can't happen, so you have $\lfloor|x|\rfloor>6$ or $|x|\geq7$ – Empy2 Apr 13 '15 at 18:34