Problem

Find the domain of the quotient of the functions \(f(x) = x^2 - 4\) and \(g(x) = x - 2\).

Answer

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Answer

Step 2: The value of \(x\) that makes \(g(x)\) equal to zero is excluded from the domain. Therefore, the domain of the quotient \(f(x) / g(x)\) is all real numbers except \(x = 2\).

Steps

Step 1 ：Step 1: Set the denominator \(g(x)\) equal to zero and solve for \(x\). \(x - 2 = 0\) implies \(x = 2\).

Step 2 ：Step 2: The value of \(x\) that makes \(g(x)\) equal to zero is excluded from the domain. Therefore, the domain of the quotient \(f(x) / g(x)\) is all real numbers except \(x = 2\).

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