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 > > > hm, what about: 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