Is the function $g (x) = x^{3} - 5 x$ $g(x) = x^3-5x$ even, odd or neither?

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Is the function $g (x) = x^{3} - 5 x$ $g(x) = x^3-5x$ even, odd or neither?

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Answer 1 · 2015-09-25T20:16:38

Rather than using a particular number or numbers, the best method is to substitute $- x$ $-x$ and simplify.

Explanation:

To determine whether $g$ $g$ if even, odd, or neither, evaluate $g (- x)$ $g(-x)$ .

If $g (- x)$ $g(-x)$ simplifies to $g (x)$ $g(x)$ , then $g$ $g$ is even. If $g (- x)$ $g(-x)$ simplifies to an equivalent to $- g (x)$ $-g(x)$ , then $g$ $g$ is odd. It may be neither even nor odd.

$g (x) = x^{3} - 5 x$ $g(x) = x^3-5x$

$g (- x) = {(- x)}^{3} - 5 (- x)$ $g(-x) = (-x)^3-5(-x)$

$= - x^{3} + 5 x$ $= -x^3+5x$

$= - (x^{3} - 5 x)$ $= -(x^3-5x)$

$= - g (x)$ $= -g(x)$ .

So, $g$ $g$ is odd.

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Is the function $g (x) = x^{3} - 5 x$ $g(x) = x^3-5x$ even, odd or neither?

1 Answer

Explanation:

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Is the function $g (x) = x^{3} - 5 x$ $g(x) = x^3-5x$ even, odd or neither?