Let f(z)=\dfrac{z+a}{z+b} and g(z)=f(f(z)), where a and b are complex numbers. Suppose that |a|=1 and g(g(z))=z for all z for which g(g(z)) is defined. What is the difference between the largest and smallest possible values of |b| ?
Answer Choices
A. 0
B. \sqrt{2}-1
C. \sqrt{3}-1
D. 1
E. 2