Subject: Compostion of functions
Who is asking: Teacher
Question: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = -x2 - 4 and g(x) = sqrt(x)
The range of f(x), x<=-4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(-x2 - 4).
In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything?
The way I would put it is: The domain is the empty set (and so is the range).
So g(f(x)) is just the empty function, with empty domain and empty range. I guess that your textbook does not want to call that a "function"; but that is just a matter of taste, and it is not very important.Claude