       Re: y=f(t) vs t=f(y)

• To: mathgroup at smc.vnet.net
• Subject: [mg6305] Re: [mg6267] y=f(t) vs t=f(y)
• From: "w.meeussen" <w.meeussen.vdmcc at vandemoortele.be>
• Date: Sat, 8 Mar 1997 00:26:28 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```At 09:49 6-03-97 -0500, Larry Smith wrote:
>     I would appreciate anyone helping me with using Mathematica to solve
>     the following (geometrically, numerically, etc)
>
>     I need to find an example of a function y=f(t) such that f'(0)=1 but t
>     is not a function of y in any neighborhood of 0.  I just arbitrarily
>     picked f'(0)=1 you could pick something with value of 1. But the trick
>     is that t is not a function of y in this neighborhood.  Any
>     suggestions?
>
>     Larry
>     larry.smith at clorox.com
>     or
>     lsmith at tcusa.net
>
>     601-939-8555 ext 255
>
>
>

t[x_]:=Which[x<=0,-1+x,x>0,1+x]

make a plot, Plot[t[x],{x,-2,2}], and you see that
the inverse function is:

x[t_]:=Which[t<-1,(t+1),t<1,0,t>=1,(t-1)]
and
Plot[x[t],{t,-3,3}]

and there you have it : the flat piece for x[t] between t=-1 and t=1
causes the function x[t] to be independent on t in that area.

Look at it again, and enjoy...
(whoever gave u this problem deserves a prize for didactics, it's a gem)

wouter

Dr. Wouter L. J. MEEUSSEN
eu000949 at pophost.eunet.be
w.meeussen.vdmcc at vandemoortele.be

```

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