Final answer:
The question's details about limits of functions f(x) and g(x) as x approaches -1 are incomplete, lacking information on how to combine these functions to find the limit. Additional information is needed to apply the correct properties of limits and compute the answer.
Step-by-step explanation:
The student has provided the limits of two functions as x approaches -1: lim _{x---> -1} f(x)=2 and lim _{x---> -1} g(x)=-6. However, the question seems to be incomplete as it does not specify which operation involving f(x) and g(x) is being asked about to find the limit. Without more information, such as whether we are looking for the sum, product, quotient, or any other combination of f(x) and g(x), we cannot provide a specific answer about the limit involving these two functions.
When provided with the complete question, we can utilize the properties of limits to find the answer. For example, if we need to find the sum of the limits, we use the property that the limit of the sum is equal to the sum of the limits. If it's the product, we use the property that the limit of the product is the product of the limits. And for a quotient, provided the limit of the denominator is not zero, the limit of the quotient is the quotient of the limits.