What are the domain restrictions of ?

The denominator :  q² - 3q - 4 should be ≠ 0.
Let's find the zero values of this quadratic equation:

q' = [-b+√(b²-4.a.c)]/2.a    and   q'' = [-b-√(b²-4.a.c)]/2.a

you will fond q' = 4  and q'' = -1

Then the restrictions are :

q ≠ 4 and q ≠ - 1 (1st answer)