Question

Anyone here good at f(x) to know if they are odd or even.....

f(x)=5x^6-7/x^3

Answer 1

So, something is even if f(x) = f(-x).
Therefore, to test if the function is even:
\[f(x) = 5x^6 - 7/x^3 \neq 5x^6 + 7/x^3 = 5(-x)^6 - 7/(-x)^3 = f(-x)\]
Since f(x) does not equal f(-x), the function is not even.

If something is odd, then f(x) = -1 * f(x)
Therefore, to test if the function is odd:
\[f(x) = 5x^6 - 7/x^3 \neq -5x^6 - 7/x^3 = -5(-x)^6 + 7/(-x)^3 = -1 * f(-x)\]
Since f(x) does not equal -1 * f(-x) the function is not odd.

Answer 2

wow, the tutorial is wanting me to substitute (x) with (-x) and work it out...