Final answer:
The domain of g(x) is all real numbers except x = -2. The domain of h(x) has no restrictions.
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. To determine the restrictions on the domain of the functions g(x) = 1/(x+2) and h(x) = 3x, we need to consider any values of x that would result in undefined or unacceptable values in the functions.
For g(x), we find that the function is undefined when the denominator (x+2) is equal to zero. Therefore, we have the restriction x+2 ≠ 0. Solving this inequality, we get x ≠ -2. So, the domain of g(x) is all real numbers except x = -2.
For h(x), there are no restrictions on the domain since it is a simple linear function with no denominators or square roots.