Determine which of the following functions are one-to-one.

A. $f:{\mathbb R}^3 \rightarrow {\mathbb R}^3$ defined by $f(x,y,z)=(x-y, y-z, x-z).$
B. $f:{\mathbb R}^3 \rightarrow {\mathbb R}^3$ defined by $f(x,y, z)=(x+y, y+z, x+z).$
C. $f:{\mathbb R} \rightarrow {\mathbb R}$ defined by $f(x)=x^2.$
D. $f:{\mathbb R} \rightarrow {\mathbb R}$ defined by $f(x)=x^3.$
E. $f:{\mathbb R}^2 \rightarrow {\mathbb R}^2$ defined by $f(x,y)=(x+y, 2x+2y).$