How do you determine whether a function is odd, even, or neither: $f (x) = \frac{2 x}{| x |}$ $f(x)= (2x)/absx$ ?

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Answer 1 · 2016-11-30T10:01:16

$f (x) = \frac{2 x}{| x |}$ $f(x) = (2x)/|x|$ is and odd function.

If $f (- x) = - f (x)$ $f(-x) = -f(x)$ then $f (x)$ $f(x)$ is odd.

If $f (- x) = f (x)$ $f(-x)=f(x)$ then $f (x)$ $f(x)$ is even.

In this case:

$f (- x) = \frac{2 (- x)}{| - x |} = - \frac{2 x}{| x |} = - f (x)$ $f(-x) = (2(-x))/|-x| =-(2x)/|x| = -f(x)$

So the function is odd.

How do you determine whether a function is odd, even, or neither: f(x)= (2x)/absx f(x)=2x|x|f(x)= (2x)/absx ?