Problem

Given the functions f(x)=x+2 and g(x)=1x−3, find the domain of the sum of the functions f(x)+g(x).

Answer

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Answer

The combined domain is the intersection of the two separate domains, which is x≥−2 and x≠3.

Steps

Step 1 ：Step 1: Find the domain of each function separately.

Step 2 ：For f(x)=x+2, the domain is x≥−2 because the expression under the square root must be greater than or equal to 0.

Step 3 ：For g(x)=1x−3, the domain is x≠3 because the denominator of a fraction cannot be 0.

Step 4 ：Step 2: Combine the two domains.

Step 5 ：The combined domain is the intersection of the two separate domains, which is x≥−2 and x≠3.

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