2) If you get stuck on a problem like this you can pick a number to substitute in to all the answer choices. For example, if I let x = 2, we get:
(A) -6 = 2
So we can eliminate (A)
(B) -8 = 8
So we can eliminate (B)
(C) -12 = -4
So we can eliminate (C)
(D) -6 = 2
So we can eliminate (D)
(E) -10 = -10
So we CAN'T eliminate (E)
Since (E) is the only one not eliminated, (E) is the answer.
(1) Be very careful substituting these in - lots of minus signs tend to lead to careless errors.
(2) You need to check EVERY answer choice - just because the two numbers agree doesn't mean that that's the correct answer. It only means you can't eliminate it.
(3) Let me do one computation in detail for you in case you're confused about how to do it. I'll do choice (A):
f(x) = x+4
f(2) = 2+4=6
-f(2) = -6
Solving the problem using actual math: The given condition says that f is an ODD function. The answer choices are all polynomials. A polynomial is an odd function if and only if all exponents are odd. Choice (E) is the only choice with all odd exponents.
Note that x has exponent 1, and a constant has exponent 0.