It’s ok if you don’t do the problem, I really just need someone to explain in simple terms how interval notation works, and if you could, how I’d relate it to the domain.
g(f(x)) = f(x)^2 + 1
= [sqrt(x – 3)]^2 + 1
= x – 3 + 1
= x + 2.
The domain of sqrt(x – 3) is values of x for which x – 3 >= 0, as sqrt(u) is not defined for negative u.
The domain is therefore x >= 3, and you write this as
A square bracket shows that the number (3 in this case) is included in the range. A round bracket shows that the number (infinity in this case) is excluded. Infinity is always excluded, as it is not a number in the true sense.