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 use the following definitions:1. A function is **even** if \( f(-x) = f(x) \) for all .2. A function is **odd** if \( f(-x) = -f(x) \) for all .3. If neither condition is satisfied, the function is **neither even nor odd**.---### Step 1: Compute \( f(-x) \)Substitute into the function \( f(x) \): Simplify the numerator and denominator:- The numerator becomes: - The denominator becomes: Thus: ---### Step 2: Compare \( f(-x) \) with \( f(x) \)The original function is: From Step 1, we found: Clearly, \( f(-x) \neq f(x) \), so the function is **not even**.Now check if \( f(-x) = -f(x) \): We see that \( f(-x) = -f(x) \). Therefore, the function is **odd**.---### Final Answer:The function \( f(x) = \frac{-x^3}{5x^2 - 6} \) is **odd**.