1. Find a continuous function 0,1) \rightarrow \mathbb {R} " alt="f0,1) \rightarrow \mathbb {R} " /> with an image equal to

I'm thinking may be something like arctanx + 1/2 ?

2. Find a continuous function 0,1) \rightarrow \mathbb {R} " alt="f0,1) \rightarrow \mathbb {R} " /> with an image equal to [0,1]

tanx?

3. Find a continuous function that is strictly increasing and has image equal to (-1,1).

Sinx might work but it ain't strictly increasing...