Is the following function even, odd, or neither? f(x)=x^(4)-2x^(2) Choose 1 answer: A) Even (B) Odd (c) Neither

Define function and determine f(-x): Define the function f(x) and determine f(-x). The function given is f(x)=x^4-2x^2. To determine if the function is even, odd, or neither, we need to evaluate f(-x) and compare it to f(x).Substitute -x in f(x): Substitute -x for x in f(x) to find f(-x). f(-x)=(-x)^4-2(-x)^2Simplify f(-x): Simplify the right side of the function. f(-x)=(-x)^4-2(-x)^2 simplifies to f(-x)=x^4-2x^2 because (-x)^4 = x^4 and (-x)^2 = x^2.Compare f(x) and f(-x): Compare f(x) and f(-x). We have f(x)=x^4-2x^2 and f(-x)=x^4-2x^2. Since f(-x) = f(x), the function f(x) is an even function.

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Is the following function even, odd, or neither?

f(x)=x^(4)-2x^(2)
Choose 1 answer:
A) Even
(B) Odd
(c) Neither

Is the following function even, odd, or neither? $\newline$ $f(x)=x^{4}-2 x^{2}$ $\newline$ Choose $1$ answer: $\newline$ (A) Even $\newline$ (B) Odd $\newline$ (C) Neither

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Algebra 2

Even and odd functions

Full solution

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

\newline

f(x)=x^{4}-2 x^{2}

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

Define function and determine f(-x): Define the function f(x) and determine f(-x). $\newline$ The function given is $f(x)=x^4-2x^2$ . To determine if the function is even, odd, or neither, we need to evaluate $f(-x)$ and compare it to $f(x)$ .
Substitute $-x$ in $f(x)$ : Substitute $-x$ for $x$ in $f(x)$ to find $f(-x)$ . $f(-x) = (-x)^4 - 2(-x)^2$
Simplify $f(-x)$ : Simplify the right side of the function. $f(-x)=(-x)^4-2(-x)^2$ simplifies to $f(-x)=x^4-2x^2$ because $(-x)^4 = x^4$ and $(-x)^2 = x^2$ .
Compare $f(x)$ and $f(-x)$ : Compare $f(x)$ and $f(-x)$ . $\newline$ We have $f(x)=x^4-2x^2$ and $f(-x)=(-x)^4-2(-x)^2$ . Since $f(-x) = f(x)$ , the function $f(x)$ is an even function.