Problem 72
Question
If the equations of two functions are given, explain how to obtain the quotient function and its domain.
Step-by-Step Solution
Verified Answer
The quotient function is obtained by dividing the first function by the second one. The domain of the quotient function consists of all real numbers except those that make the denominator zero.
1Step 1: Understanding and dividing functions
Given two functions, say \(f(x)\) and \(g(x)\), the quotient function \(h(x)\) is obtained by dividing \(f(x)\) by \(g(x)\), denoted as \(h(x) = \frac{f(x)}{g(x)}\). Simply perform the operation of division as instructed by the equation.
2Step 2: Determining the domain of the quotient function
For a quotient function, the denominator must not equals to zero. Hence, to find the domain of the quotient function, set the denominator function, i.e., \(g(x)\), equal to zero and solve for \(x\). The solutions provide the values of \(x\) that make the denominator zero. The domain of the quotient function is all real numbers except these solutions. If the results are real numbers, then they are excluded from the domain of function \(h(x)\).
Other exercises in this chapter
Problem 71
Determine whether each function is even, odd, or neither. $$f(x)=x \sqrt{1-x^{2}}$$
View solution Problem 72
Find the domain of each function. $$ f(x)=\sqrt{x^{2}-5 x-24} $$
View solution Problem 72
Show that the points \(A(1,1+d), B(3,3+d),\) and \(C(6,6+d)\) are collinear (lie along a straight line) by showing that the distance from \(A\) to \(B\) plus th
View solution Problem 72
Determine whether each function is even, odd, or neither. $$f(x)=x^{2} \sqrt{1-x^{2}}$$
View solution