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# A floor function equation M421 in CRUX

Posted 1 year ago
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Posted 3 months ago
 Hello, could you help me with my question? I have this function and I know that the range is a union of several intervals. Is there any way for Mathematica to give me the general formula of the range of this function? (Abs[x] - Floor[x])/(Sqrt[2 - Floor[x]]) I found the ranges by defining an interval for x, following the example of what you wrote. Reduce[FunctionRange[{(Abs[x] - Floor[x])/Sqrt[2 - Floor[x]], -50 <= x < 0}, x, y]] This is the plot: Plot[(Abs[x] - Floor[x])/(Sqrt[2 - Floor[x]]), {x, -20, 3}] Posted 3 months ago
 Three things to consider: Only consider one continuous subdomain for x at a time. Floor function introduces non-linearity to the solution and in general no silver bullet to kill all problems. Beware of floor function for negative numbers. Test some numbers if you find it hard to memorize the behavior Plot on small scale and use customized grid lines to visualize the boundaries for jumpy ranges. Only discuss the negative integer cases here: Of course you also need to add the range for the positive part, which is easy to handle by choosing x in [0,1) and [1,2), or k = 0 and 1.
Posted 3 months ago
 Thank you very much, sir
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