Determine whether the function f, of, x, equals, 9, x, cubed, minus, 5, x, plus, 5, x, to the power 5f(x)=9x 3 −5x+5x 5 is even, odd or neither.

To determine whether the function is even, odd, or neither, we need to apply the definitions of even and odd functions.

An even function is one where f(x) = f(-x) for all x in the domain of the function. An odd function is one where -f(x) = f(-x) for all x in the domain of the function.

The function given is f(x) = 9x^3 - 5x + 5x^5.

Let's first check if it's an even function:

f(-x) = 9(-x)^3 - 5(-x) + 5(-x)^5 = -9x^3 + 5x - 5x^5.

This is not equal to f(x), so the function is not even.

Now let's check if it's an odd function:

-f(x) = -9x^3 + 5x - 5x^5.

This is equal to f(-x), so the function is odd.

Therefore, the function f(x) = 9x^3 - 5x + 5x^5 is an odd function.