Is the function b(x) = 3x^3 - x even, odd, or neither? Choices: (A)even (B)odd (C)neither

Check Even Function: Check if b(x) is even by evaluating b(-x) and comparing it to b(x). b(-x) = 3(-x)^3 - (-x)Simplify b(-x): Simplify b(-x). b(-x) = -3x^3 + xCompare Even Functions: Compare b(-x) with b(x). b(x) = 3x^3 - x b(-x) = -3x^3 + x Since b(-x) is not equal to b(x), b(x) is not even.Check Odd Function: Check if b(x) is odd by evaluating if b(-x) is equal to -b(x). -b(x) = -(3x^3 - x)Simplify -b(x): Simplify -b(x). -b(x) = -3x^3 + xCompare Odd Functions: Compare -b(x) with b(-x). -b(x) = -3x^3 + x b(-x) = -3x^3 + x Since -b(x) is equal to b(-x), b(x) is odd.

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Is the function $b(x) = 3x^3 - x$ even, odd, or neither? $\newline$ Choices: $\newline$ (A)even $\newline$ (B)odd $\newline$ (C)neither

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Algebra 2

Even and odd functions

Full solution

Q. Is the function

b(x) = 3x^3 - x

even, odd, or neither?

\newline

Choices:

\newline

(A)even

\newline

(B)odd

\newline

(C)neither

Check Even Function: Check if $b(x)$ is even by evaluating $b(-x)$ and comparing it to $b(x)$ . $\newline$ $b(-x) = 3(-x)^3 - (-x)$
Simplify $b(-x)$ : Simplify $b(-x)$ . $b(-x) = -3x^3 + x$
Compare Even Functions: Compare $b(-x)$ with $b(x)$ . $\newline$ $b(x) = 3x^3 - x$ $\newline$ $b(-x) = -3x^3 + x$ $\newline$ Since $b(-x)$ is not equal to $b(x)$ , $b(x)$ is not even.
Check Odd Function: Check if $b(x)$ is odd by evaluating if $b(-x)$ is equal to $-b(x)$ . $-b(x) = -(3x^3 - x)$
Simplify $-b(x)$ : Simplify $-b(x)$ . $-b(x) = -3x^3 + x$
Compare Odd Functions: Compare $-b(x)$ with $b(-x)$ .
$-b(x) = -3x^3 + x$
$b(-x) = -3x^3 + x$
Since $-b(x)$ is equal to $b(-x)$ , $b(x)$ is odd.