Test for even: If even, then F(-x) = F(x)
F(-x) = 2(-x)^2 - 4(-x) - 1 = 2x^2 + 4x -1
therefore, F(-x) does NOT equal F(x) and function is NOT even.
If odd, then F(-x) = -F(x)
But -F(x) = -2x^2 + 4x +1 which does NOT equal F(-x)
Therefore the function is NEITHER
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