Problem

Given two functions f(x)=x2−4 and g(x)=2x−4, find the domain of the quotient function h(x)=f(x)g(x).

Answer

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Answer

Step 3: Exclude the value x=2 from the combined domain of f(x) and g(x) since g(2) equals zero. Therefore, the domain of h(x) is all real numbers except x=2.

Steps

Step 1 ：Step 1: Identify the domain of the individual functions. For f(x), the domain is all real numbers since f(x) is a polynomial. For g(x), the domain is also all real numbers since g(x) is a linear function. Therefore, the combined domain of f(x) and g(x) is all real numbers.

Step 2 ：Step 2: Identify any values that would make g(x) equal to zero since division by zero is undefined. Set g(x) equal to zero and solve for x: 2x−4=0⇒x=2

Step 3 ：Step 3: Exclude the value x=2 from the combined domain of f(x) and g(x) since g(2) equals zero. Therefore, the domain of h(x) is all real numbers except x=2.

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