Chapter 2 - Nonlinear Functions - 2.1 Properties of Functions - 2.1 Exercises - Page 55: 69

$ f(x)$ is odd.

$ f(x)$ is odd if $f(-x)=-f(x)$ $ f(x)$ is even if $f(-x)=f(x)$ ------------- $f(x)=\displaystyle \frac{x}{x^{2}-9}$ $f(-x)=\displaystyle \frac{-x}{(-x)^{2}-9}=-\frac{x}{x^{2}-9}$ $=-f(x)$ $ f(x)$ is odd.