Question

for the following exercise, determine whether the function is odd, even, or neither.
$f(x)=7x^{4}$
odd even neither
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question 2
for the following exercise, determine whether the function is odd, even, or neither.
$f(x)=6x - x^{3}$
odd even neither
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Explanation:

Step1: Recall even - odd function definitions

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

Step2: Check $f(x) = 7x^{4}$ for even - ness

Substitute $-x$ into $f(x)$: $f(-x)=7(-x)^{4}=7x^{4}=f(x)$. So it's even.

Step3: Check $f(x)=6x - x^{3}$ for even - ness/odd - ness

Substitute $-x$ into $f(x)$: $f(-x)=6(-x)-(-x)^{3}=-6x + x^{3}=-(6x - x^{3})=-f(x)$. So it's odd.

Answer:

Question 1: even
Question 2: odd