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Is the following function even, odd, or neither?

f(x)=2|x|-5
Choose 1 answer:
(A) Even
(B) Odd
(c) Neither

Is the following function even, odd, or neither? $\newline$ $f(x)=2|x|-5$ $\newline$ 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)=2|x|-5

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

(C) Neither

Determine Even, Odd, Neither: To determine if the function $f(x)$ is even, odd, or neither, we need to compare $f(x)$ with $f(-x)$ . If $f(x) = f(-x)$ for all $x$ , then the function is even. If $f(x) = -f(-x)$ for all $x$ , then the function is odd. If neither condition is met, the function is neither even nor odd.
Find $f(-x)$ : Let's find $f(-x)$ by substituting $-x$ for $x$ in the function $f(x)=2|x|-5$ .
$f(-x) = 2|-x|-5$
Since the absolute value of $-x$ is the same as the absolute value of $x$ ( $|x| = |-x|$ ), we can simplify this to:
$f(-x) = 2|x|-5$
Compare $f(x)$ and $f(-x)$ : Now we compare $f(x)$ and $f(-x)$ :
$f(x) = 2|x| - 5$
$f(-x) = 2|-x| - 5$
We can see that $f(x)$ and $f(-x)$ are the same for all $x$ . Therefore, the function $f(x)$ is even.

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