Does the function $f(x) = \frac{x^2-1}{x-1}$ have any point discontinuity?
49368
Why does factoring eliminate a hole in the limit?
132730
Is there an everywhere discontinuous increasing function?
24306
Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
24449
How discontinuous can a derivative be?
127125
Can the limit $\lim_{h \to 0}\frac{f(x + h) - 2f(x) + f(x - h)}{h^2}$ exist if $f'(x)$ does not exist at $x$?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
118400
Is there a monotonic function discontinuous over some dense set?
60700
Continuity of a function to the integers
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
133231
Discontinuity of Thomae Function on $\mathbb{Q}$
22392
How can a function with a hole (removable discontinuity) equal a function with no hole?
62744
Does the functional equation $f(1/r) = rf(r)$ have any nontrivial solutions besides $f(r) = 1/\sqrt{r}$?
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
144773
function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct?
150005
Existence of points in a differentiable function
41043
example of discontinuous function having direction derivative
143874
Limit of derivative is zero. Does it imply a limit for f(x)?