Results 1 to 3 of 3

Math Help - Continuous but not differentiable

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    28

    Smile Continuous but not differentiable

    Give an example of 2 continuous functions f : R \rightarrow R satisfying f(0)=g(0)=0 and such the composition f \circ g is differentiable at x=0 but neither f nor g is differentiable at x=0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Aug 2009
    Posts
    28
    Quote Originally Posted by DaRush19 View Post
    Give an example of 2 continuous functions f : R \rightarrow R satisfying f(0)=g(0)=0 and such the composition f \circ g is differentiable at x=0 but neither f nor g is differentiable at x=0.
    This was meant to say: Give an example of 2 continuous functions f : R \rightarrow R and g: R \rightarrow R satisfying...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2009
    Posts
    113
    Define f(x)=g(x)=\frac{1}{x} if x\neq 0 and f(0)=g(0)=0. We have f\circ g(x)=x
    for all x\in \mathbb{R}. Neither f nor g is continuous at 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. continuous/differentiable
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 8th 2010, 10:19 AM
  2. Replies: 0
    Last Post: October 3rd 2010, 08:03 AM
  3. continuous - differentiable question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 28th 2009, 07:55 PM
  4. differentiable, f' not continuous
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 21st 2009, 07:08 AM
  5. continuous, not differentiable
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 22nd 2008, 03:56 PM

Search Tags


/mathhelpforum @mathhelpforum