# Range of Even Function

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.

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

• Thank you so much for your fruitful help. – Waqar Ali Shah Jan 17 '18 at 13:58

How about $x^{2m} \cos(nx)$ a bit of generalization I think.

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