#xsinx# is even or odd,?

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Answer 1 · 2018-05-10T08:53:13

Even

An even function is defined as one which:
#f(x)=f(-x)#

An odd function is defined as one which:
#f(-x)=-f(x)#

We have #f(x)=xsinx#

#f(-x)=-xsin(-x)#

Due to the nature of #sinx#, #sin(-x)=-sinx#

So, #f(-x)=-x*-sinx=xsinx=f(x)#

#f(x)=f(-x)#

#xsinx# is therefore even,