The domain of a function is the set of all possible input values (x-values) that the function can accept without leading to any mathematical inconsistencies such as division by zero or square roots of negative numbers. In your case, both functions f(x) and g(x) are linear functions defined as f(x) = x + 6 and g(x) = x + 6, respectively.
Since both f(x) and g(x) are defined for all real numbers, we can say:
- For f(x) = x + 6, all x values will provide a defined output.
- For g(x) = x + 6, similarly, all x values will yield a defined output.
The product of two functions, h(x) = f(x) * g(x), combines both inputs. Since the product involves multiplication and there are no restrictions on the values of x from either f(x) or g(x), the resulting function h(x) will also be defined for all real numbers.
Therefore, the domain of h(x) = f(x) * g(x) is also all real numbers.