How do you determine if $f(x)= |x^3+x| - Cos x$ is an even or odd function?

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Answer 1 · 2016-08-14T02:14:59

Even function.

If (f(-x) = f(x) , f(x) is an even function.

Here,

$f(-x)$

$=|-x+(-x)^3|-cos(- x)$

$=|-(x+x^3)|-cos x$

$=|x+x^3|-cos x$

$=fx)$ .

So, f is even.

How do you determine if f(x)= |x^3+x| - Cos xf(x)= |x^3+x| - Cos x is an even or odd function?