Warren,

Since (f/g)(x) = f(x)/g(x) for x to be in the domain of (f/g)(x) it must be in the domain of f and in the domain of g. You also need to insure that g(x) is not zero since f(x) is divided by g(x). Thus there are 3 conditions.

x must be in the domain of f: f(x) = 3x -5 and all real numbers x are in the domain of x.

x must be in the domain of g: g(x) = √(x - 5) so x - 5 ≥ 0 so x ≥ 5.

g(x) can not be 0: g(x) = √(x - 5) and √(x - 5) = 0 gives x = 5 so x ≠ 5.

Hence to satisfy all three conditions x x ≥ 5 and x ≠ 5 so the domain of (f/g)(x) is all x satisfying x > 5.

Penny