do you actually remember what the arctan(x) graph looks like? it is not arctan(x) that should be used here, the range for that graph is certainly not all real numbers, it is

you want tan(x) here. but it will be transformed somehow. see if you can figure out how

here is where you might choose a shifted arctan(x) graph. but consider using something simpler, like a transformed sine or cosine graph2. Find a continuous function 0,1) \rightarrow \mathbb {R} " alt="f0,1) \rightarrow \mathbb {R} " /> with an image equal to [0,1]

tanx?

a transformed arctan(x) will work nicely here. sine or cosine won't work3. Find a continuous function that is strictly increasing and has image equal to (-1,1).

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