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.