Problem 105 - College Algebra

Question

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

Step-by-Step Solution

Answer

The quotient function is obtained by dividing one function by another i.e. \(h(x) = \frac{f(x)}{g(x)}\). It's domain is the set of all real numbers except for those values of \(x\) that makes the denominator \(g(x) = 0\).

Step 1: Understand the concept of Quotient function

A quotient function of two functions \(f(x)\) and \(g(x)\) would be in the form \(h(x) = \frac{f(x)}{g(x)}\). It thus involves dividing the function \(f(x)\) by \(g(x)\)

Step 2: Obtain the Quotient function

The quotient function can be found by directly dividing the function \(f(x)\) by \(g(x)\). This should be done carefully to ensure that every component of the function is properly divided.

Step 3: Identify the Domain of the Quotient function

The domain of the quotient function is the set of all real numbers that allows the function to be defined. Here the denominator \(g(x)\) cannot be equal to zero, because division by zero is undefined in Real Numbers. So for the quotient function to be defined, all \(x\) where \(g(x) \ne 0\) form the domain of the quotient function.