to determine whether a given function is even, we simply substitute x with -x in the expression. if the result after simplification is identical to the original equation, then the function is said to be even other wise odd.
f(-x) = (-x)^2 - (-x) + 8
= x^2 + x +8
the resulting function is not identical to the original one;
f(-x) ≠ f(x)
therefore, f(x) is not an even function