real analysis - Find a bijection between the open interval (0, 1) and the closed interval [0, 1].

This was part of a three part question where I was supposed to prove two sets have equal cardinality by finding bijections. I've created a bijection $f: \Bbb Z \Rightarrow 2\Bbb Z$ by $f(x)=2x$. I've created a bijection $g: (0,1) \Rightarrow (4,50)$ by $g(x)=46x+4$. I think those are both correct. My last question is finding a a bijection between (0,1) and [0,1]. I've seen this question several times on this board, but I've yet to understand them and I can't really go back and ask any questions to the original posters. I know a bijective function exists between (0,1) and $\Bbb R$, but I don't think that helps me here.