Problem

Find the domain of the difference of the functions f(x)=x−1 and g(x)=1x+2.

Answer

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Answer

Therefore, the domain of f(x)−g(x) is the set of all x such that x≥1 and x≠−2. Since 1>−2, the second condition is automatically satisfied when x≥1.

Steps

Step 1 ：To find the domain of the difference of the functions f(x)−g(x), we need to find the set of all real numbers that are in both the domain of f(x) and the domain of g(x).

Step 2 ：The function f(x)=x−1 is defined for all x such that x−1≥0. Solving this inequality gives x≥1.

Step 3 ：The function g(x)=1x+2 is defined for all x such that x+2≠0. Solving this equation gives x≠−2.

Step 4 ：Therefore, the domain of f(x)−g(x) is the set of all x such that x≥1 and x≠−2. Since 1>−2, the second condition is automatically satisfied when x≥1.

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