Bunuel wrote:

For which of the following functions does f(−x)=−f(x) for all real number values of x?

A. x^8−x^4

B. x^2−x^6

C. x^5/x^7

D. x^9/(x^5+1)

E. x^5/(x^2+1)

Kudos for a correct solution.

A. f(-x) = (-x)^8 - (-x)^4 is

not equal to -f(x) = -(x^8 - x^4).

B. option B has a similar structure to option A's answer choice!− f(-x) = (-x)^2 - (-x)^6 which is

not equal to -f(x) = -(x^2 - x^6).

C. f(-x) = (-x)^5/(-x)^7 is also

not equal to -f(x) = -(x^5/x^7). f(-x) yields a + answer, whilst -f(x) yields a − answer.

D. f(-x) = (-x)^9/((-x)^5+1) is

not equal as -f(x) = (-1)*x^9/(x^5+1).

E. f(-x) = (-x)^5/((-x)^2+1) is

equal to -f(x) = (-1)*x^5/(x^2+1), because (-x)^5 is equal to (-1)*x^5 and ((-x)^2+1) is the same as (x^2+1).

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