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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}]
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Three things to consider:
- Only consider one continuous subdomain for
xat 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.
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Thank you very much, sir
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