19.1.1.12 Properties of metric spaces

Condition: let \ (\ rho (x, y)- \) metric on the set \ (x \). Prove that the functions \ [\ begin {array} {l} \ rho_ {1} (x, y) = \ frac {\ rho (x, y)} {1+ \ rho (x, y)} \\ \ rho_ {2} (x, y) = \ ln (1+ \ rho (x, y)), \\ \ rho_ {3} = \ min \ {1, \ rho (x, y) \} \ end {array} \] are also metrics.