Questions: Consider the functions F and G as shown in the graph to the right. Find the domain of G/F. What is the domain of G/F? (Type your answer in interval notation.)

Consider the functions F and G as shown in the graph to the right. Find the domain of G/F. What is the domain of G/F? (Type your answer in interval notation.)
Transcript text: Consider the functions F and G as shown in the graph to the right. Find the domain of G/F. What is the domain of G/F? $\square$ (Type your answer in interval notation.)
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Solution

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Solution Steps

Step 1: Identify the Domain of F and G
  • The domain of F is the set of x-values for which F is defined. From the graph, F is defined for x-values: {2, 4, 6, 8, 10, 12}.
  • The domain of G is the set of x-values for which G is defined. From the graph, G is defined for x-values: {2, 4, 6, 8, 10}.
Step 2: Determine the Common Domain
  • The domain of G/F is the intersection of the domains of F and G. Therefore, the common domain is {2, 4, 6, 8, 10}.
Step 3: Exclude Points Where G(x) = 0
  • For the function G/F to be defined, G(x) must not be zero. From the graph, G(x) is zero at x = 10.

Final Answer

  • The domain of G/F is {2, 4, 6, 8}, which in interval notation is: \[2, 4, 6, 8\].
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