Question

Determine the combined domain (\( \text{Dom } (F ∩ G) \)) of functions \( F \) and \( G \) given \( \text{Dom } F = ℝ - \{-2, 8\} \) and \( \text{Dom } G = ℝ \).

a) \( ℝ - \{-2, 8\} \)
b) \( \{-2, 8\} \)
c) \( ℝ \)
d) \( ∅ \)

Answer 1

The combined domain of functions F and G, where Dom F is all real numbers except -2 and 8, and Dom G is all real numbers, is ℝ - \{-2, 8\} since G poses no additional restrictions on the domain.

Step-by-step explanation:

To determine the combined domain (Dom (F ∩ G)) of functions F and G where Dom F = ℝ - \{-2, 8\} and Dom G = ℝ, we must look for the intersection of these two domains. Since the domain of G includes all real numbers, and the domain of F includes all real numbers except -2 and 8, the combined domain is determined by the restrictions of F since those are the most restrictive conditions.

The correct answer is that the combined domain is the set of all real numbers except for -2 and 8, which can be represented as ℝ - \{-2, 8\}.

This tells us that the combined domain is the same as the domain of function F, because function G poses no additional restrictions.

Therefore, the correct choice is (a) ℝ - \{-2, 8\}.