Question

question 3
for the following exercise, determine whether the function is odd, even, or neither.
f(x)=4x^4
odd even neither
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question 4
for the following exercise, determine whether the function is odd, even, or neither.
f(x)=8\sqrt{x}
odd even neither
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Explanation:

Question 3

Step1: Recall even - function definition

A function $f(x)$ is even if $f(-x)=f(x)$. For $f(x) = 4x^{4}$, substitute $-x$: $f(-x)=4(-x)^{4}$.

Step2: Simplify the expression

Since $(-x)^{4}=x^{4}$, then $f(-x)=4x^{4}=f(x)$.

Step1: Recall the domain and function - property definitions

The domain of $y = f(x)=8\sqrt{x}$ is $x\geq0$. For a function to be odd or even, the domain must be symmetric about the origin. Since negative values are not in the domain of $f(x)=8\sqrt{x}$, it cannot satisfy $f(-x)=f(x)$ (even - function property) or $f(-x)=-f(x)$ (odd - function property).

Answer:

even

Question 4