Question

Domain and range of f(x)=(x+1)^2+7

Answer 1

to find the domain you need to ask "are there any values of x that make f(x) undefined?"
things that make a function undefined are:
dividing by zero
taking the square root of a negative number
taking the logarithm of zero or a negative number

are there any values of x that cause this to happen? if so what are they?
if not, the answer would be that "the function is defined on all reals"