a question on differentiability
in [Math]
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From: Ron on 1 Jun 2010 10:25 On Jun 1, 10:13 am, dushya <sehrawat.dushy...(a)gmail.com> wrote: > On Jun 1, 7:03 am, Ron <ron.sper...(a)gmail.com> wrote: > > > On Jun 1, 9:32 am, dushya <sehrawat.dushy...(a)gmail.com> wrote: > > > > suppose f:A->B ; g:A->C and h:C->B be such that f = hog > > > > by composite function theorem if h and g are differentiable then so is > > > f but does differentiability of f and g imply differentiability of h ? > > > or does differentiability of f and h imply differentiability of g ? > > > > please reply. > > > Hint: Consider constant functions. > > hey thanks :-) but suppose we have two more conditions g(A)=C, f(A)=B.. Okay. still false. (Consider f(x)=x,g(x)=x^(1/3),h(x)=x^3 or switch g,h if desired)
From: Timothy Murphy on 1 Jun 2010 10:28 dushya wrote: >> > suppose f:A->B ; g:A->C and h:C->B be such that f = hog >> >> > by composite function theorem if h and g are differentiable then so is >> > f but does differentiability of f and g imply differentiability of h ? >> > or does differentiability of f and h imply differentiability of g ? >> >> > please reply. >> >> Hint: Consider constant functions. > > hey thanks :-) but suppose we have two more conditions g(A)=C, f(A)=B. What if B consists of a single point? -- Timothy Murphy e-mail: gayleard /at/ eircom.net tel: +353-86-2336090, +353-1-2842366 s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
From: dushya on 1 Jun 2010 10:35
On Jun 1, 7:25 am, Ron <ron.sper...(a)gmail.com> wrote: > On Jun 1, 10:13 am, dushya <sehrawat.dushy...(a)gmail.com> wrote: > > > On Jun 1, 7:03 am, Ron <ron.sper...(a)gmail.com> wrote: > > > > On Jun 1, 9:32 am, dushya <sehrawat.dushy...(a)gmail.com> wrote: > > > > > suppose f:A->B ; g:A->C and h:C->B be such that f = hog > > > > > by composite function theorem if h and g are differentiable then so is > > > > f but does differentiability of f and g imply differentiability of h ? > > > > or does differentiability of f and h imply differentiability of g ? > > > > > please reply. > > > > Hint: Consider constant functions. > > > hey thanks :-) but suppose we have two more conditions g(A)=C, f(A)=B. > > Okay. still false. (Consider f(x)=x,g(x)=x^(1/3),h(x)=x^3 or switch > g,h if desired) thank you Ron. |