How do you know if # f(x)=x^2+sin x# is an even or odd function?

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Answer 1 · 2016-01-23T11:52:33

#f(x)# is not EVEN neither ODD

Given #f(x)#:

#f(x)# is EVEN if: #f(-x)=f(x)#

#f(x)# is ODD if:#f(-x)=-f(x)#

In the question:

#f(x)=x^2+sin(x)#

#:. f(-x)=(-x)^2+sin(-x)=x^2-sin(x)!=f(x)#
#f(-x)!=-f(x)#

#=> f(x)# is not EVEN neither ODD