How to determine which of the following functions are one-to-one ?

See explanation...

A. ##f## is not one-one. The function maps all the points of ##RR^3## to the plane ##x+y+z = 0##.

For example:

##f(1, 1, 1) = (1-1, 1-1, 1-1) = (0, 0, 0) = (2-2, 2-2, 2-2) = f(2, 2, 2)##

B. ##f## is not one-one since it is an even function ##f(-1) = 1 = f(1)##

C. ##f## is one-one (essentially a rotation and scaling) with inverse ##f^(-1)(x, y, z) = ((x-y+z)/2, (y-z+x)/2, (z-x+y)/2)##

D. ##f## is one-one (a rotation and scaling) with inverse ##f^(-1)(x, y) = ((x+y)/2, (x-y)/2)##

E. ##f## is not one-one ##f(1) = 1 - 1 = 0 - 0 = f(0)##