Q. about regular language

Question

Let L be a regular language

Is the language L2={y: there exist x and z  such that |x|=|z| and xyz belons to L} regular?

Comments

arrange question properly not readable

Answer 1

I think it should be regular, $L_2 = L$

by putting $x = z = \epsilon$ .

Answer 2

Q.Is the language L2={y: there exist x and z  such that |x|=|z| and xyz belons to L} regular?

A. yes it should be regular since length is equal

example

1. take any string aab

    here x= a, y= a, z= b

2.  take another string aabab

 here x= aa, y= b,  z=ab

any string can be broken into xyz such that x ans z is equal .

Comments

yes it should be regular if |x| = |z| = epsilon