Final answer:
The domain of g(x) = -f(x+7) will be the same as the domain of f(x), because the operation x+7 is defined for all real numbers. If f(x) is defined for all real numbers, then g(x) too, whereas if f(x) is only defined for x greater than 0, then g(x) would be defined for x> -7.
Explanation:
The domain of the function g(x) = -f(x+7) is defined as the set of all possible inputs (x-values) for which the function is defined. Since the given function, g(x), involves another function, f(x), we will need to know the domain of f(x) to figure out the domain of g(x). Essentially, the domain of g(x) will be the same as the domain of f(x), because the operation x+7 is defined for all real numbers.
For example, if f(x) is defined for all real numbers, then g(x) would also be defined for all real numbers. But if f(x) is only defined for x greater than 0, for example, then g(x) would be defined for x> -7.
