help!! it says: Determine if f(x)=4x^(2/3) is even, odd, or neither?

Answer 1

Neither.

note, for instance, that f(-1) is undefined;
thus, nethier
f(-1) = f(1)
nor
f(-1) = -f(1)

is true.

Answer 2

I disagree with both previous answers.

Assuming that x>0 so that you're only dealing with real numbers, then regardless of the result of x^(2/3) when you multiply it by 4 then the product is divisible by 2 since 4 is divisible by 2.

Hence, for x>=0; f(x) is even.

Btw, zero is even.

Answer 3

It is either even or irrational. If x^(2/3) is an integer (example 8^(2/3)=4), any integer multiplied by 4 is even.

Answer 4

f(-x) = f(x), so f(x) is even