I have a very interesting question:
Given a function $f$ which is continuous but need not be differentiable.
Then the correct statement is
a. it can be an odd function
b. it can't be an invertible function
c. it can be an invertible function
By just examining $f(x) = x$ it is an odd function which is differentiable. I rule out a.
Also $\mod x$ is not be invertible and not differentiable. So somehow I believe that the answer should be b.
Basically what should be my approach?
What is the proper way of examining this type of question?
Also is there any relationship between differentiable and invertible functions?
Thank you.
a) f could be a triangle wave -- odd, continuous, not-differentiable.
b) or c) must be true. So which is it?
A bijective function is invertable. Can you come up with a bijection that is continuous but not differentiable?
$f(x) = \begin{cases} x&x<0\\2x &x\ge0\end{cases}$