How do you determine if #f(x)= 2x / |x|# is an even or odd function?

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Answer 1 · 2016-07-06T04:02:47

Neither.

For real x, #y =f (x)=2x/|x|=2#, for #x>0 and f(x) = - 2 #, for #x<0#.

The graph consists of two half lines #y =+- 2# in the first and third

quadrants, respectively, with break at #(0, +-2)#.

If x is complex, #x = r e^(itheta) and f(x) = 2(re^(itheta))/r=2e^(itheta)#

#=2(cos theta + i sin theta)#

Here, #cos theta# is even and #sin theta# is odd, and therefore, f(x)

is neither odd nor even.