The domain of f(x) · g(x) is all real numbers except x = 2.
How to determine the domain of the product of two functions
In this problem we must determine the domain of the product of two functions: f(x), g(x), that is, the set of all values such that resulting function exists. First, we determine the domain of each function:
Dom {f(x)} = All real numbers
Dom {g(x)} = All real numbers except x = 2.
Second, determine the domain of the product of the two functions: (The set of common x-elements)
Dom {f(x) · g(x)} = All real numbers except x = 2.