1. The problem statement, all variables and given/known data Find an explicit homeomorphism from (0,1) to R. 2. Relevant equations A homeomorphism from (-1,1) to R is f(x)=tan(pi*x/2). 3. The attempt at a solution I'm horrible a modifying trig functions. Obviously, to shift by b you add b to (x) and you can change the frequency by including a scalar to pi. I tried f(x)=tax(2pi*(x+1)/2), but this doesn't do the trick.