I have a two part question that I'm not quite sure how to approach... it goes as follows:

1. Prove that (R^n, d) is a metric space, where:

d_mb(x,y) =d_m(x,y)/(d_m(x,y) +1)

2. Find the unit ball B_M(0; 1) for M = (R^3, d), where d is the distance function defined in 1.

Any help would be appreciated! Thank you!