Problem 1:The hyperbolic line consists of positive real numbers with the hyperbolic distance defined as the absolute value of . Show the composition of isometries of the hyperbolic line is an isometry of the hyperbolic line.
Problem 2:
The hyperbolic line consists of positive real numbers with the hyperbolic distance defined as the absolute value of . Suppose f is an isometry of the hyperbolic line. Can you give a formula for f ?