Question

How do i tell if y=x^3+x^2 is even or odd?

Answer 1

If a function is even, then f(-x) = x.

If a function is odd, then f(-x) = -x.

y = x³ + x² → f(x) = x³ + x² → -f(x) = -(x³ + x²) = -x³ - x²

f(-x) = (-x)³ + (-x)² = [(-1)(x)]³ + [(-1)(x)]² = (-1)³x³ + (-1)²x²

= -1x³ + 1x² =-x³ + x²

f(-x) ≠ f(x) and f(-x) ≠ -f(x)

y = x³ + x² is not odd and not even

Answer: neither