Question

determine whether the function f(x)=-x^3 - 7 is even, odd or neither.

Explanation:

Step1: Recall the definitions

An even function satisfies $f(-x)=f(x)$ and an odd function satisfies $f(-x)=-f(x)$.

Step2: Find $f(-x)$

Substitute $-x$ into $f(x)$: $f(-x)=-(-x)^{3}-7 = x^{3}-7$.

Step3: Compare with $f(x)$ and $-f(x)$

We have $f(x)=-x^{3}-7$. And $-f(x)=x^{3}+7$. Since $f(-x)
eq f(x)$ and $f(-x)
eq -f(x)$, the function is neither even nor odd.

Answer:

Neither