# Continuous but not differentiable

• September 1st 2009, 10:16 AM
DaRush19
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 $x=0$.
• September 1st 2009, 10:19 AM
DaRush19
Quote:

Originally Posted by DaRush19
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...
• September 1st 2009, 10:24 AM
Enrique2
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.