Is #(absx-7)/(x^3-x)# odd, even, or neither?

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Answer 1 · 2017-02-09T15:11:10

Odd

Change x to #-x#.

#f(-x)=(|-x|-7)/((-x)^3-(-x))#

#=-(|x|-7)/(x^3-x)#

#=-f(x)#.

So, f is odd.

The graph of odd functions are symmetric about O.

See the inserted Socratic graph for f(x).

graph{(|x|-7)/(x^3-x) [-10, 10, -5, 5]}