question_answer 20)

Show that the Modulus function f : given by f(x) = |x|, is neither one one nor onto, where |x| is, if x position or 0 and |x| is ? x, if x is negative.  

Answer:

f(x) = |x|       Let x1 = 1 and x2 = ? 1 be two real numbers             f(x1) = f(1) = |1| = 1;             f(x2) = f(-1) = |-1| = 1                     Also, let y = ? 1             which is not possible as |x| is always positive.        is not onto.