Geometry

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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 ?
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