I need help with the following problem:

Show the function

f(x) = x / (1 + |x|) is a bijection

f: R -> (-1, 1)

I know that f(b) = f(a) => b = a... and if you can show this then the function is a bijection. I know I'm forgetting something obvious, but the absolute value in the function is throwing me for a loop.

Thank you for help you can offer.