Respuesta :
Answer:
To determine whether the function h(x) = (-x^3) / (3x^2 - 9) is even or odd, we need to examine how it behaves when the variable x is replaced by -x.
1. Even Function: A function is even if it satisfies the property h(x) = h(-x) for all x in its domain. In other words, if substituting -x for x in the function equation gives the same result as the original function, then the function is even.
2. Odd Function: A function is odd if it satisfies the property h(x) = -h(-x) for all x in its domain. In this case, if substituting -x for x in the function equation gives the negative of the original function's value, then the function is odd.
Now, let's analyze the function h(x):
h(x) = (-x^3) / (3x^2 - 9)
To determine if it is even or odd, we need to check whether h(x) is equal to h(-x) or -h(-x).
Let's substitute -x for x in the function:
h(-x) = (-(-x)^3) / (3(-x)^2 - 9)
= (-(-x)^3) / (3x^2 - 9)
Comparing h(-x) to the original function h(x), we can see that h(x) is not equal to h(-x) or -h(-x).
Therefore, the function h(x) = (-x^3) / (3x^2 - 9) is neither even nor odd.
