Finding a continuous function and a sequentially compact Is there such a continuous function $f: R\rightarrow R $ and a sequentially compact $K \subset R$ such that the inverse $f^{-1}(K)$ is not sequentially compact? 

Could someone provide me with some examples so I can get a better understanding of sequentially compact?
Hint: If you choose sin x as your function what would you choose for $K$? $[-\pi/2, \pi/2]$?
Hint: If you choose sin x as your function what would you choose for $K$? $[-\pi/2, \pi/2]$?