Having the definition: A function $f:\mathbb{R^n}\rightarrow \mathbb{R^n}$ is proper if $\|f(x)\|$ tends to $\infty$ when $\|x\|$ tends to $\infty$. I have to show :
a)If $f:\mathbb{R^n}\rightarrow \mathbb{R^n}$ is proper and continuous , the inverse image of a compact set is compact;
b) If $f:\mathbb{R^n}\rightarrow \mathbb{R^n}$ is proper and continuous , show that $f$ attains its minimum.
I am really stuck (I can't get started...).Some explanation is welcome.Thanks.