Question

I need help determining if this function is odd, even, or neither. Please provide steps!!!

f(x) = 3√x

Answer 1

A function is considered odd if for every value x in its domain, the function satisfies the condition f(-x) = -f(x). A function is considered even if for every value x in its domain, the function satisfies the condition f(-x) = f(x). If a function doesn't satisfy either of these conditions, then it is considered neither odd nor even.

Step-by-step explanation:

A function is considered odd if for every value x in its domain, the function satisfies the condition f(-x) = -f(x). A function is considered even if for every value x in its domain, the function satisfies the condition f(-x) = f(x). If a function doesn't satisfy either of these conditions, then it is considered neither odd nor even.

In the case of the function f(x) = 3√x:

1. Substitute -x for x in the function and simplify:
f(-x) = 3√(-x) = 3i√(|x|) (where i represents the imaginary unit)

2. Substitute x for x in the function and simplify:
f(x) = 3√x

Since f(-x) is not equal to -f(x) and also not equal to f(x), the function f(x) = 3√x is neither odd nor even.