How do you determine whether the graph of $f (x) = \frac{1}{5 x} - x^{19}$ $f(x)=1/(5x)-x^19$ is symmetric with respect to the origin?

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Answer 1 · 2016-11-25T14:46:50

Monomials with odd exponents are odd functions, and so is their sum.

You can verify that by noting that:

$f (- x) = (- 1) \frac{1}{5 x} - {(- 1)}^{19} x^{19} = - f (x)$ $f(-x) = (-1) 1/(5x) - (-1)^19x^19 = -f(x)$

How do you determine whether the graph of f(x)=15x−x19f(x)=1/(5x)-x^19 is symmetric with respect to the origin?