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Is the function $t(x) = -4x^7 + 2x$ 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

t(x) = -4x^7 + 2x

even, odd, or neither?

\newline

Choices:

\newline

(A)even

\newline

(B)odd

\newline

(C)neither

Check Even Function: Check if $t(x)$ is even by evaluating $t(-x)$ and comparing it to $t(x)$ . $\newline$ $t(-x) = -4(-x)^7 + 2(-x)$
Simplify $t(-x)$ : Simplify $t(-x)$ . $t(-x) = -4(-x)^7 + 2(-x) = 4x^7 - 2x$
Compare $t(-x)$ and $t(x)$ : Compare $t(-x)$ with $t(x)$ . $\newline$ $t(x) = -4x^7 + 2x$ $\newline$ $t(-x) = 4x^7 - 2x$ $\newline$ Since $t(-x)$ is not equal to $t(x)$ , $t(x)$ is not even.
Check Odd Function: Check if $t(x)$ is odd by evaluating if $t(-x)$ is equal to $-t(x)$ . $-t(x) = -(-4x^7 + 2x) = 4x^7 - 2x$
Compare $-t(x)$ and $t(-x)$ : Compare $-t(x)$ with $t(-x)$ .
$-t(x) = 4x^7 - 2x$
$t(-x) = 4x^7 - 2x$
Since $t(-x)$ is equal to $-t(x)$ , $t(x)$ is odd.

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