       Re: How to invert a function of several variables?

• To: mathgroup at smc.vnet.net
• Subject: [mg114649] Re: How to invert a function of several variables?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 11 Dec 2010 01:56:12 -0500 (EST)

```Use Reduce, NSolve, or FindRoot. For example,

f[x_, y_] :== Sin[Sqrt[x^2 + y^3 + 6]]^2

x[fv_?NumericQ, y_?NumericQ] :==

Last /@ List @@ (Reduce[f[x, y] ==== fv, x] /. C -> 0)

x[1/4, 0] // Quiet

{-Sqrt[-6 + (49*Pi^2)/36], Sqrt[-6 + (49*Pi^2)/36], (-I)*Sqrt[6 - Pi^2/36],
I*Sqrt[6 - Pi^2/36], -Sqrt[-6 + (25*Pi^2)/36], Sqrt[-6 + (25*Pi^2)/36]}

f[#, 0] & /@ %

{1/4, 1/4, 1/4, 1/4, 1/4, 1/4}

Bob Hanlon

<serge-ars at yandex.ru> wrote:

==========================
Honorable ladies and gentlemen,

I need to invert a real function of two real variables f(x, y) with respect to the first variable x, while the second variable y is fixed. The function is rather difficult, so Mathematica can't invert it symbolically, and I need at least to invert it numerically.

Thank you.
serge-ars at yandex.ru

```

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