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Question

Is f(x)=xx2+2|x|+1 is an odd function

Solution
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Let f(x)=xx2+2|x|+1

Put x=x in f(x)

As (x)2=x2 and |x|=|x| we get

f(x)=xx2+2|x|+1

f(x)=(xx2+2|x|+1)

f(x)=f(x)

So, f(x) is an odd function

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