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

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Answer 1 · 2015-11-29T18:13:45

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)#