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Chapter 2: Problem 105

If equations for two functions are given, explain how to obtain the quotient function and its domain.

Short Answer

Expert verified
The quotient function \(h(x)\) is obtained by dividing \(f(x)\) by \(g(x)\), that is, \(h(x) = f(x) / g(x)\). The domain of the quotient function is all real numbers except for those values that make \(g(x)\) equal to zero.

Step by step solution

01

Identify the functions

Firstly, identify the two functions, say \(f(x)\) and \(g(x)\). These will be provided in the problem statement.
02

Get the quotient function

The quotient function \(h(x)\) is obtained by dividing \(f(x)\) by \(g(x)\), that is, \(h(x) = f(x) / g(x)\). This gives the quotient function.
03

Determine the domain of the quotient function

The domain of the quotient function is all real numbers except for those values that make \(g(x)\) equal to zero. This is because we cannot divide by zero. So, solve the equation \(g(x) = 0\) and exclude the solutions (if any) from the set of real numbers. This gives the domain of the quotient function.

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