Is the domain for this expression correct?

The domain of the function will include everything x CAN be. Since in a fraction, you cannot have zero in the denominator, you have to set the denominator =0.
So, x^2-13x+42=0
Then factor that
(x-6)(x-7)=0
So, x-6=0 and x-7=0
Then x=6 and x=7 are the two times this function is undefined. So, it's domain actually encludes more than listed:
(-inf,6)U(6,7)U(7,inf)
You can include what's in between 6 and 7, just not 6 and 7 itself... therefore, the open brackets (parentheses)

(-inf,6) U (6,7) U (7, inf)

U shoudl add numbers between 6 and 7 too.
Add this : (6,7)
Only 6 and 7 cannot be included