Problems with FindRoot and recursive functions

• To: mathgroup at smc.vnet.net
• Subject: [mg89641] Problems with FindRoot and recursive functions
• From: "Daniel Kuang Chen Liu" <dkliu1 at student.monash.edu.au>
• Date: Mon, 16 Jun 2008 06:39:03 -0400 (EDT)

```Hello,

I have a recursive function of the form

>> x1[t_] := If[t < 0, {t, 1}, 0.5 + x1[t - 1]]

which returns a list of length 2, and the first element has a root at t=0.5
>> In[3]:= x1[0.5]
>> Out[3]= {0., 1.5}

I want to use FindRoot to determine t0 such that x1[t0][[1]] == 0, so I use
the following code

>> FindRoot[x1[t][[1]] == 0, {t, 0.5}]

to which Mathematica complains

During evaluation of In[6]:= FindRoot::nlnum: The function value
{False} is not a list of numbers with dimensions {1} at {t} = {0.5}.

It would much appreciated if someone could tell me what is wrong with the
code.

Daniel Liu

```

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