Is the following function even, odd, or neither? f(x)=(3)/(x^(2)+2) Choose 1 answer: (A) Even (B) Odd (C) Neither

Define function and f(-x): Define the function f(x) and determine f(-x). The given function is f(x)=(3)/(x^(2)+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 for x in f(x)=(3)/(x^(2)+2). f(-x)=(3)/((-x)^(2)+2)Simplify f(-x): Simplify f(-x). Simplify the right side of the function by noting that (-x)^2 is equal to x^2 because the square of a negative number is positive. f(-x)=(3)/(x^(2)+2)Compare f(x) and f(-x): Compare f(x) and f(-x). We have: f(x)=(3)/(x^(2)+2) f(-x)=(3)/(x^(2)+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)=(3)/(x^(2)+2)
Choose 1 answer:
(A) Even
(B) Odd
(C) Neither

Is the following function even, odd, or neither? $\newline$ $f(x)=\frac{3}{x^{2}+2}$ $\newline$ 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)=\frac{3}{x^{2}+2}

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

Define function and $f(-x)$ : Define the function $f(x)$ and determine $f(-x)$ . The given function is $f(x)=\frac{3}{x^{2}+2}$ . To determine if the function is even, odd, or neither, we need to evaluate $f(-x)$ and compare it to $f(x)$ . Substitute $-x$ for $x$ in $f(x)=\frac{3}{x^{2}+2}$ . $f(-x)=\frac{3}{(-x)^{2}+2}$
Simplify $f(-x)$ : Simplify $f(-x)$ . Simplify the right side of the function by noting that $(-x)^2$ is equal to $x^2$ because the square of a negative number is positive. $f(-x)=\frac{3}{x^{2}+2}$
Compare $f(x)$ and $f(-x)$ : Compare $f(x)$ and $f(-x)$ . We have: $f(x)=\frac{3}{x^{2}+2}$ $f(-x)=\frac{3}{x^{2}+2}$ Since $f(-x) = f(x)$ , the function $f(x)$ is an even function.