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Thread: Continuous but not differentiable

  1. #1
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    Smile Continuous but not differentiable

    Give an example of 2 continuous functions $\displaystyle f : R \rightarrow R$ satisfying $\displaystyle f(0)=g(0)=0$ and such the composition $\displaystyle f \circ g$ is differentiable at $\displaystyle x=0$ but neither f nor g is differentiable at $\displaystyle x=0$.
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  2. #2
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    Quote Originally Posted by DaRush19 View Post
    Give an example of 2 continuous functions $\displaystyle f : R \rightarrow R$ satisfying $\displaystyle f(0)=g(0)=0$ and such the composition $\displaystyle f \circ g$ is differentiable at $\displaystyle x=0$ but neither f nor g is differentiable at $\displaystyle x=0$.
    This was meant to say: Give an example of 2 continuous functions $\displaystyle f : R \rightarrow R$ and $\displaystyle g: R \rightarrow R$ satisfying...
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  3. #3
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    Define $\displaystyle f(x)=g(x)=\frac{1}{x}$ if $\displaystyle x\neq 0$ and $\displaystyle f(0)=g(0)=0$. We have $\displaystyle f\circ g(x)=x$
    for all $\displaystyle x\in \mathbb{R}$. Neither $\displaystyle f$ nor $\displaystyle g$ is continuous at 0.
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