Question

is the function g(x) = 2x^7 - x^5 - 6x^3 even, odd, or neither? even odd neither

Explanation:

Step1: Recall the definitions

A function \( g(x) \) is even if \( g(-x) = g(x) \) for all \( x \) in the domain. A function \( g(x) \) is odd if \( g(-x) = -g(x) \) for all \( x \) in the domain.

Step2: Compute \( g(-x) \)

Given \( g(x) = 2x^7 - x^5 - 6x^3 \), substitute \( -x \) for \( x \):

$$
LATEXBLOCK0
$$

Step3: Compare with \( -g(x) \)

Compute \( -g(x) \):

$$
LATEXBLOCK1
$$

We see that \( g(-x) = -g(x) \).

Answer:

odd