Can someone show the work with some details that $f^{-1}$ is not continuous at $(1,0)$?
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
115417
Continuity of $L^1$ functions with respect to translation
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
154881
Question on differentiability of a continuous function
21301
If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
142870
Prove the function is not differentiable at (0,0)
158888
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$.
117419
Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
30860
Prove that $f(x)=0$ in $[-1,1]$.
135199
Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous
61486
Show that $f$ is not differentiable at $(0,0)$ - $\frac{x_1^2x_2}{x_1^2+x_2^2}$
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
136011
Must $f$ be continuous?
70790
Evaluation of $\lim_{q \to 0} (\int_0^1 |f|^q)^{1/q} $ for $f \in L^1([0,1])$.
150554
proof that $f'$ is continuous at $a$
65876
A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete