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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