Final answer:
An odd function is a function that satisfies the property f(x) = -f(-x), and out of the given options, the odd function is f(x) = 6x^3 + 2x.
Step-by-step explanation:
An odd function is a function that satisfies the property f(x) = -f(-x). In other words, if you replace x with -x in the function and negate the result, it should be equal to the original function.
Now let's apply this definition to the given functions:
- f(x) = 3x^2 + x
- f(x) = 4x^3 + 7
- f(x) = 5x^2 + 9
- f(x) = 6x^3 + 2x
Out of these options, the odd function is f(x) = 6x^3 + 2x. When you replace x with -x and negate the result, it will be equal to the original function.