im very vERY confused..

first of all,can anyone confirm to me if 'maximal' domain and 'domain' are the same?

i am trying to find maximal domain & range of these on the real line:

F(x) = x² + 2x – 3

F(x) = √ x² + 2x – 3

F(x) = 1/√ x² + 2x – 3

F(x) = (x² + 2x – 3) -⅓

aren't they all going to be the same?

factorising you get = (x+3)(x-1)

so domain is the whole real line except -3, 1

and range will be whole real line...! where am i going wrong.....

thankyou!