Question

Which type of function is F(x) = 2x^3 - (x/3x^4 + 5x^2)?

A) Even
B) Odd
C) Neither even nor odd
D) Insufficient information

Answer 1

The given function f(x) = 2x^3 - (x/3x^4 + 5x^2) is neither even nor odd.

Step-by-step explanation:

An odd function is a function where the value of f(-x) is equal to -f(x) for all x in the domain of the function. On the other hand, an even function is a function where the value of f(-x) is equal to f(x) for all x in the domain of the function.

Let's analyze the given function f(x) = 2x^3 - (x/3x^4 + 5x^2).

To determine if the function is even or odd, we need to check if f(-x) = f(x) or f(-x) = -f(x).

Calculating f(-x), we have f(-x) = 2(-x)^3 - (-x)/(3(-x)^4 + 5(-x)^2).

Simplifying this expression, we get f(-x) = -8x^3 + x/(3x^4 + 5x^2).

As we can see, f(-x) is not equal to f(x) or -f(x), which means that the given function f(x) = 2x^3 - (x/3x^4 + 5x^2) is neither even nor odd.