Re: A problem with FindRoot

*To*: mathgroup at smc.vnet.net*Subject*: [mg83789] Re: A problem with FindRoot*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Fri, 30 Nov 2007 05:28:03 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <fim7qp$qqp$1@smc.vnet.net>

Vassilis Dimitrakas wrote: > I'd like some help with respect to a problem I have with the FindRoot, > NSolve and FindInstance functions. > My version of Mathematica is 5.2 > > I define the function f as follows: > > f[x_]:={ > y/.FindRoot[y^3+1==x,{y,x}][[1]] > }[[1]] > > f[x] returns the root of the equation y^3 + 1 == x, i.e. the value > (x-1)^(1/3). f[x] has obviously a > unique root at x=1. > > If I now try to find f[x]'s root with FindRoot, for example like > > FindRoot[f[x]==0,{x,3}] > > Mathematica (v 5.2) returns error messages and no solution. The same > happens if I use instead NSolve > or FindInstance. Can you guys explain why this happens and suggest a > remedy? I bet that the error messages you get are a similar to "FindRoot::srect: "Value x in search specification {y,x} is not a number or array of numbers." Add a condition to your definition of f so it is called only for numeric arguments. In[1]:= Clear[f] f[x_?NumberQ] := {y /. FindRoot[y^3 + 1 == x, {y, x}][[1]]}[[1]] FindRoot[f[x] == 0, {x, 3}, AccuracyGoal -> 5] Out[3]= {x -> 1.} Regards, -- Jean-Marc