If a (x) = 3x + 1 and b (x) = squareroot x-4, what is the domain of (b*a) (x) ?

I am a bit confused with the "*", but I think you want to calculate this composite function: b (a (x)), where a (x) = 3x+1 & b (x) & b (x) = √ (x-4), if so:

b (a (x)) = b (3x+1) = = > b (a (x)) = √[ (3x+1) - 4] = = > b (a (x)) = √ (3x-3)

This function is valid for 3x-3> = 0 = = > x> = 1, then the domain of this composite function is all real number >=1