Range of Even Function

Question

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.

score 6 · Answer 1 · answered Jan 17 '18 at 11:50

6

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

answered Jan 17 '18 at 11:50

Mostafa Ayaz

31,924

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

score 2 · Answer 2 · edited Jan 17 '18 at 14:37

2

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

edited Jan 17 '18 at 14:37

egreg

238,574

answered Jan 17 '18 at 14:02

Devendra Singh Rana

1,780
1
15
32

Thanks for your help. What are the values of m? I think the values of n are integers. – Waqar 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

Range of Even Function

2 Answers2