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I want to print the values of y for a range of x for an implicit function f(x,y). My equation is f(x,y)=x^2+y^2+2. The range of x is (2,10). I want the corresponding values of y.

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    $\begingroup$ An implicit equation needs to be of the form x^2 + y^2 + 2 = Constant in order to be solved. In your equation y is unconstrained meaning it can be literally any value. To find actual values for y, we need to be able to rearrange the equation into something like y = ± Sqrt[Constant - x^2 - 2]. $\endgroup$ – MassDefect Dec 4 '18 at 18:23
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As pointed out earlier, if your equation is in the form x^2 + y^2 + 2 = Constant, then you can solve for y:

Clear[x, y];
eq = x^2 + y^2 + 2 == 0
sol = Solve[eq, y]

{{y -> -Sqrt[-2 - x^2]}, {y -> Sqrt[-2 - x^2]}}

These solutions can then be evaluated at some x-values of your choosing:

Table[{x, y /. sol}, {x, 2, 10}] // MatrixForm

![enter image description here

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Before starting to Solve as in @MelaGo's solution, I would recommend you define and discretize an implicit region to get an idea of where the $xy$ values are:

J = ImplicitRegion[x^2 + y^2 + 2 == 5, {x, y}];
DiscretizeRegion[J, Frame -> True]

enter image description here

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Using InverseFunction:

ClearAll[f]
f[x_, y_] := x^2 + y^2 + 2
finv = Quiet @ InverseFunction[f, 2, 2]

-Sqrt[-2 - #1^2 + #2] &

TableForm[Table[Row[{1, -1} finv[i, k], ","], {i, 1, 10}, {k, {5, 50, 100}}], 
 TableHeadings -> {"x = " <> ToString @ # & /@ Range[2, 10], 
   " f[x, y] = " <> ToString @ # & /@ {5, 50, 100}}]

enter image description here

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As @MassDefect has pointed out, you need to constrain y to some value (it can be dependent on x, but the relationship must be known). If you are just asking how to input a function and have it print the result you can try the following

myFunction[x0_,y0_] := Module[{x=x0,y=y0},
x^2 + y^2 +2];

For[i=2, i<11, i++,
Print[myFunction[i,3]]]

Note in my code i have specified y=3, but you could have a line directly above it saying y=x^2 -5 or something similar and then replace the 3 in the Print function with y.

Hope this helps

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