Is $\frac{| x | - 7}{x^{3} - x}$ $(absx-7)/(x^3-x)$ odd, even, or neither?

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Answer 1 · 2017-02-09T15:11:10

Odd

Change x to $- x$ $-x$ .

$f (- x) = \frac{| - x | - 7}{{(- x)}^{3} - (- x)}$ $f(-x)=(|-x|-7)/((-x)^3-(-x))$

$= - \frac{| x | - 7}{x^{3} - x}$ $=-(|x|-7)/(x^3-x)$

$= - f (x)$ $=-f(x)$ .

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]}

Is (absx-7)/(x^3-x)|x|−7x3−x(absx-7)/(x^3-x) odd, even, or neither?