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[1] -> 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