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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 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 by step solution

01

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 \(g(x)\)
02

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.
03

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.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(f(x)=x^{3}\) and \(g(x)=-(x-3)^{3}-4,\) then the graph of \(g\) can be obtained from the graph of \(f\) by moving \(f\) three units to the right, reflecting about the \(x\) -axis, and then moving the resulting graph down four units.

What must be done to a function's equation so that its graph is shifted horizontally to the right?

Begin by graphing the standard cubic function, \(f(x)-x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\frac 12(x-3)^{3}-2 $$

Begin by graphing the absolute value function, \(f(x)-|x| .\) Then use transformations of this graph to graph the given function. $$ g(x)--2|x+4|+1 $$

Show that $$ f(x)=\frac{3 x-2}{5 x-3} $$ is its own inverse.
See all solutions

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