Final answer:
The domain of f(x) is (-∞, 0) U (0, ∞). The domain of g(x) is [0, ∞). The domain of F o G is [3, ∞).
Step-by-step explanation:
The domain of a function is the set of all possible input values or x-values for the function. In the case of f(x) = 1/x, since we cannot divide by zero, the domain is all real numbers except for x = 0. Therefore, the domain of f(x) is (-∞, 0) U (0, ∞).
For the function g(x) = √x - 3, the domain is determined by the square root. We cannot take the square root of a negative number, so the expression under the square root (√x) must be greater than or equal to zero. This means that x ≥ 0. Therefore, the domain of g(x) is [0, ∞).
To find F o G, we substitute g(x) into f(x). So, F o G = f(g(x)) = f(√x - 3) = 1/(√x - 3). Note that because of the square root, the expression under the square root (√x - 3) must be greater than or equal to zero. This means that x ≥ 3. Therefore, the domain of F o G is [3, ∞).
Learn more about Domain of Functions