which of the following statements are true
let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\sin x^3$. then $f$ is continuous but not uniformly continuous.
every differentiable function $f:(0,1)\to[0,1]$ is uniformly continuous.
$f:X\to Y$ be a continuous map between metric spaces. if $f$ is a bijection, then its inverse is also continuous.
my thoughts:
true as its derivative is unbounded.
false example is $x^2\sin(1/x)$.
false.
please somebody confirm me about my thinkings. thank you.