Question

If g(x) = 3x −1 and f(x) = sqrt(9-x^2) then which of the following will have a domain of: [−3, 1/3) ∪ (1/3, 3]?
A. (g + f)(x)
B. (f/g)(x)
C. (g − f)(x)
D. g(f(x))
E. f(g(x))

Answer 1

Well, if you look at any of the compositions or additions or subtractions, you're only going to have one domain restriction, and that is the square root. So the domain might be some number to infinity or -infinity to some number.

But you have TWO domain restrictions, this suggests a rational function.