Let \( f(x)=\frac{x}{x^{2}-6} \). Determine \( f(-x) \) first and then determine whether the function is even, odd, or neither. Write even if the function is even, odd if the function is odd, and neither if the function is neither even nor odd. \( f(-x)= \) Even/Odd/Neither:

To find \( f(-x) \), we substitute \(-x\) into the function: \[ f(-x) = \frac{-x}{(-x)^{2}-6} = \frac{-x}{x^{2}-6} \] Now, we compare \( f(-x) \) with \( f(x) \). We have: \[ f(x) = \frac{x}{x^{2}-6} \] and found that: \[ f(-x) = \frac{-x}{x^{2}-6} \] Notice that: \[ f(-x) = -f(x) \] This indicates that the function is **odd**. So, the final answers are: \( f(-x) = \frac{-x}{x^{2}-6} \) Odd