Which characteristic is correct for the function f (x) = 4x5+8x+2f (x) = 4x5+8x+2?

neither even nor odd

odd

even

both even and odd

A function is odd if and only if y=f (x) is the same as y=-f (-x). Also a function is said to be even if and only if y=f (x) is the same as y=f (-x).

given our function f (x) = 4x^5+8x+2

-f (-x) = - (4 (-x) ^5+8 (-x) + 2)

=4x^5+8x-2

also,

f (-x) = 4 (-x) ^5+8 (-x) + 2

=-4x^5-8x+2

from the above we see that f (x) ≠ - f (-x) and also f (x) ≠ f (-x). We therefore conclude that the function is neither even not odd