How do you determine if $| x |$ $absx$ is an even or odd function?

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Answer 1 · 2016-05-30T20:11:13

$| x |$ $abs(x)$ is an even function.

A function $f (x)$ $f(x)$ is even if $f (- x) = f (x)$ $f(-x) = f(x)$ for all $x$ $x$ in its domain.

A function $f (x)$ $f(x)$ is odd if $f (- x) = - f (x)$ $f(-x) = -f(x)$ for all $x$ $x$ in its domain.

In our example, we have:

$| - x | = | x |$ $abs(-x) = abs(x)$

for any value of $x$ $x$ .

So $| x |$ $abs(x)$ is an even function.

How do you determine if |x|absx is an even or odd function?