Question

determine whether the function $f(x)=4x^{4}-4x^{3}-x^{2}$ is even, odd or neither.

Explanation:

Step1: Recall the definitions

A function $f(x)$ is even if $f(-x)=f(x)$ and odd if $f(-x)=-f(x)$.

Step2: Find $f(-x)$

Substitute $-x$ into $f(x)=4x^{4}-4x^{3}-x^{2}$. We get $f(-x)=4(-x)^{4}-4(-x)^{3}-(-x)^{2}=4x^{4}+4x^{3}-x^{2}$.

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

Since $f(-x)=4x^{4}+4x^{3}-x^{2}
eq f(x)=4x^{4}-4x^{3}-x^{2}$ and $f(-x)=4x^{4}+4x^{3}-x^{2}
eq -f(x)=-4x^{4}+4x^{3}+x^{2}$, the function is neither even nor odd.

Answer:

Neither