Question

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

Answer 1

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