How do you determine if # abs (x)/ x# is an even or odd function?

2 Answers
P dilip_k
Mar 20, 2016

we know
#|x|=-x# when #x<0 #
and#|x|=x# when #x>0 #
so for #f(x)=|x|/x#
putting #x=-x#

#f(-x)=|-x|/-x=-|x|/x=-f(x)#

so it is an odd function

A. S. Adikesavan
Mar 20, 2016

x = 0 is a point of graph-breaking-discontinuity. For x > o, y = #|x|/x = x/x = 1# and for x < 0, y = #-x/x=-1#. Sans x= 0, y is an odd function.

Explanation:

Answer is brief but self-explanatory.

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