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FunctionRange[Cos[Abs[x]] - 2 Abs[Sin[x]], x, y] // FullSimplify

Why is there such a prompt when using the above code to calculate the value range of a function?

FunctionRange::eopt: Unable to find the exact range. Returning bounds on the range computed using optimization methods.

and get the result:

-Sqrt[5] <= y <= 1

enter image description here

The result obtained by the software is correct based on the calculation process in the above image, and the function is symmetric about the line x=pi,And the period of the function is 2pi. Why would prompt content still appear?

enter image description here

To eldo:

FunctionRange[Sin[RealAbs[x]] + RealAbs[Sin[x]], x, y]

When using RealAbs to calculate the value range of the above functions, the prompt still exists. What is the reason?

enter image description here

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  • $\begingroup$ In the 2nd case RealAbs returns 0. <= y <= 2. and Abs returns 1.59995*10^-11 <= y <= 2.. I don't know why this small difference exists. I also don't know why RealAbs handles the first case silently, but issues a warning in the 2nd case. $\endgroup$
    – eldo
    Commented Jan 31 at 12:50

1 Answer 1

Reset to default
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RealAbs gives the result without warning (see documentation details)

FunctionRange[Cos[RealAbs[x]] - 2 RealAbs[Sin[x]], x, y] // FullSimplify

enter image description here

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  • $\begingroup$ Why does using Abs have no effect on function graphs? $\endgroup$
    – csn899
    Commented Jan 31 at 12:08
  • $\begingroup$ @csn899 Plotting is an inherently numerical process. Once you plug in real numbers, there is no discernible difference between Abs and RealAbs. $\endgroup$
    – MarcoB
    Commented Jan 31 at 12:16

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