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Is it possible for an even function to have the entire set of real numbers as the range? I thought much about it but I didn't find. Please explain if anybody knows.

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Take $f(x)=x\sin x$ as what you want!

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  • $\begingroup$ Thank you so much for your fruitful help. $\endgroup$ – Waqar Ali Shah Jan 17 '18 at 13:58
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How about $x^{2m} \cos(nx)$ a bit of generalization I think.

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  • $\begingroup$ Thanks for your help. What are the values of m? I think the values of n are integers. $\endgroup$ – Waqar Ali Shah Jan 17 '18 at 15:18
  • $\begingroup$ m is natural no. and yes n can be any integer. $\endgroup$ – Devendra Singh Rana Jan 17 '18 at 16:09

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