elementary set theory - Bijection between [a,b) and [a,b] intervals.

I need help with finding a bijection between these two intervals: [a,b) and [a,b]. It is told that a,b are in R (real numbers). I know how to construct a bijection if a,b are integers, but i have no idea how to do it if they are real. Any ideas?

Edit: If anyone is still watching, can you tell me if I'm doing this right?

So the bijection will be f(x) = 1) a if x = a and 2) b/p-1 if x != a and x = b/p , where p is in R - {0}.

By taking the p from R - {0} and not from N, I think this could work for real numbers.

Because a < b, every number from a to b can be written as b/p. So the function moves every number upwards if I express myself that way, thus reaching the b.