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Is the function $r(x) = 3x^6 + x^2$ even, odd, or neither? $\newline$ Choices: $\newline$ (A)even $\newline$ (B)odd $\newline$ (C)neither

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Even and odd functions

Full solution

Q. Is the function

r(x) = 3x^6 + x^2

even, odd, or neither?

\newline

Choices:

\newline

(A)even

\newline

(B)odd

\newline

(C)neither

Define function $r(x)$ : $r(x) = 3x^6 + x^2$ $\newline$ Select the function for $r(-x)$ . $\newline$ Substitute $-x$ for $x$ in $r(x) = 3x^6 + x^2$ . $\newline$ $r(-x) = 3(-x)^6 + (-x)^2$
Substitute $-x$ in $r(x)$ : $r(-x) = 3(-x)^6 + (-x)^2$ $\newline$ Simplify the right side of the function. $\newline$ $r(-x) = 3x^6 + x^2$
Simplify $r(-x)$ : We have: $\newline$ $r(x) = 3x^6 + x^2$ $\newline$ $r(-x) = 3x^6 + x^2$ $\newline$ Is the function $r(x)$ even, odd, or neither? $\newline$ Since $r(-x) = r(x)$ , $r(x)$ is an even function.

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