Question

Let (X;d) be a metric space. Determine all k such that
a) kd is a metric on X.
b) k+d is a metric on X.

Answer 1

@myko

Answer 2

Also this is old for me...:). As much as I remmeber...
d is a metric if it satisfyes folowing properties:
for any x, y and z that belong to X:
d(x,x)=0
d(x,y)=d(y,x)
d(x,z)<=d(x,y)+d(y,z) triangular property
so find k that keeps this properties right

Answer 3

@walters