I assume the expression is . The absolute extrema occur at critical numbers such that or is undefined.
As you can see, there are no critical numbers such that . There is a critical number such that is undefined, namely . However, is not contained in the open interval . Therefore, there are no critical numbers and, consequently, no extrema.
Note as x approaches 0 from the right, f(x) approaches . And as x approaches 1 from the left f(x) approaches - . However, I wouldn't consider these the absolute maximum and minimum values of f(x) on the open interval 0 < x < 1 because f(x) does not actually take on those values.