Determine algebraically whether the function is even odd, or neither. f(x)=(-x^3)/(5x^2)-6

To determine whether the function \( f(x) = \frac{-x^3}{5x^2 - 6} \) is even, odd, or neither, we need to analyze the function's behavior under the transformation .1. **Even Function**: A function \( f(x) \) is even if \( f(-x) = f(x) \) for all in the domain of .2. **Odd Function**: A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all in the domain of .Let's compute \( f(-x) \): Simplify the expression: Now compare \( f(-x) \) with \( f(x) \): Clearly, \( f(-x) \neq f(x) \), so the function is not even.Next, check if \( f(-x) = -f(x) \): We see that \( f(-x) = -f(x) \). Therefore, the function \( f(x) = \frac{-x^3}{5x^2 - 6} \) is an odd function.So, the function is **odd**.