Re: Nullcline and getting "2" values for y

*To*: mathgroup at smc.vnet.net*Subject*: [mg81503] Re: [mg81468] Nullcline and getting "2" values for y*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Wed, 26 Sep 2007 06:38:49 -0400 (EDT)*References*: <28556801.1190690438836.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

A function of y has ONE value for each y. (By definition of the term "function".) What you mean to say, I think, is that there are two solutions to a certain equation. You haven't mentioned any such equation specifically, = but... if I have to guess, I'd say you mean something like fun = (b c y - a y^n + y^(1 + n))/(b + y^n); f == fun f == (10 y - 11 y^5 + y^6)/(10 + y^5) Solving for y in terms of f gives up to SIX solutions, none of which are expressible in radicals: roots = y /. Solve[f == fun, y] // ToRadicals {Root[-10 f + 10 #1 + (-11 - f) #1^5 + #1^6 &, 1], Root[-10 f + 10 #1 + (-11 - f) #1^5 + #1^6 &, 2], Root[-10 f + 10 #1 + (-11 - f) #1^5 + #1^6 &, 3], Root[-10 f + 10 #1 + (-11 - f) #1^5 + #1^6 &, 4], Root[-10 f + 10 #1 + (-11 - f) #1^5 + #1^6 &, 5], Root[-10 f + 10 #1 + (-11 - f) #1^5 + #1^6 &, 6]} Plot[roots, {f, -5, 1}] Plot[roots, {f, -50, 10}] Plot omits complex results, so those give an incomplete picture of the situation. Bobby On Mon, 24 Sep 2007 03:21:14 -0500, sean_incali <sean_incali at yahoo.com> wrote: > I have this equation I can plot using the following > > ClearAll["Global`*"] > > > fun = (b c y - a y^ n + y^(1 + n))/(b + y^n); > d = 0.1; > c = 1; > b = 10; > a = 11; > n = 5; > ParametricPlot[{fun, (y)}, {y, 0, 1}, PlotRange -> All] > > I am plotting the function "fun" against values of y. > > When I do that I get a curvew that clearly shows that, for a given > value of y, I should get two value for the function. > > How do I get what they are? > > If I just go.. > > d = 0.1; > c = 1; > b = 10; > a = 11; > n = 2; > y = 0.5; > > (b c y - a y^ n + y^(1 + n))/(b + y^n) > > I get > > 0.231707 > > but starting at y=0 all the way to y= 0.6 or so, there are two values! > (according to the graph) > > How do I get what those values are? > > > Thanks for any input. > > sean > > > -- DrMajorBob at bigfoot.com