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Is the following function even, odd, or neither?

f(x)=x^(3)-4x
Choose 1 answer:
(A) Even
(B) Odd
(c) Neither

Is the following function even, odd, or neither? $\newline$ $f(x)=x^{3}-4 x$ $\newline$ Choose $1$ answer: $\newline$ (A) Even $\newline$ (B) Odd $\newline$ (C) Neither

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Even and odd functions

Full solution

Q. Is the following function even, odd, or neither?

\newline

f(x)=x^{3}-4 x

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

(C) Neither

Determine Function Type: To determine if the function $f(x)$ is even, odd, or neither, we need to compare $f(x)$ with $f(-x)$ . If $f(-x) = f(x)$ , then the function is even. If $f(-x) = -f(x)$ , then the function is odd. If neither condition is met, the function is neither even nor odd.
Substitute $-x$ for $x$ : First, let's find $f(-x)$ by substituting $-x$ for $x$ in the function $f(x)=x^3-4x$ . $f(-x)=(-x)^3-4(-x)$
Simplify $f(-x)$ : Now, simplify the expression for $f(-x)$ .
$f(-x)=(\text{-}x)^3+4x$
$f(-x)=\text{-}x^3+4x$
Compare $f(x)$ with $f(-x)$ : We have the original function $f(x)=x^3-4x$ and the transformed function $f(-x)=-x^3+4x$ . Comparing $f(x)$ with $f(-x)$ , we see that $f(-x)$ is not equal to $f(x)$ and $f(-x)$ is not equal to $-f(x)$ . Therefore, the function $f(x)$ is neither even nor odd.

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\newline

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\newline

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