Problem

Given the functions f(x)=1x+2 and g(x)=x2−4, find the domain of the product of the functions h(x)=f(x)g(x).

Answer

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Answer

Step 3: The domain of the product of the functions is the intersection of the domains of each of the functions. So, it's the intersection of x∈(−∞,−2)∪(−2,+∞) and x∈(−∞,+∞).

Steps

Step 1 ：Step 1: First determine the domain of each function separately. For f(x), the denominator cannot be 0, so x+2≠0, which leads to x≠−2. So the domain of f(x) is x∈(−∞,−2)∪(−2,+∞).

Step 2 ：Step 2: For g(x), since it is a quadratic function, its domain is all real numbers, i.e., x∈(−∞,+∞).

Step 3 ：Step 3: The domain of the product of the functions is the intersection of the domains of each of the functions. So, it's the intersection of x∈(−∞,−2)∪(−2,+∞) and x∈(−∞,+∞).

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