19.1.1.3 Properties of Metric Spaces

Condition: whether the following functions are metric on the material line: a) \ (\ rho (x, y) = \ sin ^{2} (x-y) \) \ (\ rho (x, y) = \ sqrt {| x-y |} \) c) \ (x, \ rho (x, \ rho (x, \ rho (x, \ rho (x, \ rho y) = \ left | e^{x} -e^{y} \ right |.