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Suppose, for the sake of keeping things as simple as possible, that I have the following equation that I wish to simplify in Mathematica:

$y = x x$

But suppose further that I also have a restriction, not directly on $x$, but on what values $y$ can have. More specifically, let's suppose $y \leq 9$.

What Mathematica expression, if any, will allow me to simplify the above expression for $y$ and get an output that not only simplifies, but also gives me the range of values that $x$ can take to satisfy my restriction on $y$?

So, just to be clear, the function or script I am looking for will output something like the following when dealing with the above:

y = $x^2$ and $-3\leq x\leq3$

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  • $\begingroup$ Can you give an example of a simple right hand side $xx$? $\endgroup$ – bill s Nov 17 '18 at 10:27
  • $\begingroup$ I literally mean x time x. That is just to provide the most basic case.If I see the procedure, I can most likely work on more difficult problems. $\endgroup$ – user120911 Nov 17 '18 at 11:16
  • $\begingroup$ There is nothing to simplify in this your example. Maybe it is much too simple? Could you give a more complex one where some simplification can be done? $\endgroup$ – Alexei Boulbitch Nov 17 '18 at 15:53
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You can use FunctionDomain:

FunctionDomain[{x^2, x^2<=9}, x]

-3 <= x <= 3

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Is this what you are looking for?

Reduce[y == x x && y <= 9, y, Reals]
(* -3 <= x <= 3 && y == x^2 *)
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