SOLUTION: To determine if a function is odd even or neither. f(x) = x^3 - x^2. Ok substitute (-x)^3 - (-x)^2 -x^3 + x^2. How can I determine if it is odd even or neither. to me it is mix

Algebra ->  Functions -> SOLUTION: To determine if a function is odd even or neither. f(x) = x^3 - x^2. Ok substitute (-x)^3 - (-x)^2 -x^3 + x^2. How can I determine if it is odd even or neither. to me it is mix      Log On


   

Question 730189: To determine if a function is odd even or neither.
f(x) = x^3 - x^2. Ok substitute (-x)^3 - (-x)^2
-x^3 + x^2. How can I determine if it is odd even or neither. to me it is mixed the x^3 becomes, -x^3 and x^2 becomes -x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
It's neither because there's a mix of odd and even exponents.

If it was even, then you'd have all even exponents.

If it was odd, then you'd have all odd exponents.

This trick only works for polynomials.

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f(x) = x^3 - x^2

f(-x) = (-x)^3 - (-x)^2

f(-x) = -x^3 - x^2

So f(x) does NOT equal f(-x) which means that f(x) is NOT even.

f(x) = x^3 - x^2

-f(x) = -(x^3 - x^2)

-f(x) = -x^3 + x^2

-f(x) = -x^3 + x^2

So f(-x) does NOT equal -f(x) which means that f(x) is NOT odd.

Final answer: f(x) is neither even nor odd.