Divide functions

Learning Objectives Define the quotient of two functions, (f/g)(x). Correctly use the notation (f/g)(x) = f(x) / g(x). Algebraically divide two functions, including polynomial and radical functions. Determine the domain of a quotient function by considering the domains of the original functions and the restriction that the denominator cannot be zero. Evaluate a quotient function at a specific input value, such as finding (f/g)(c). Simplify the resulting quotient function through algebraic techniques like factoring. Ever wondered how businesses calculate the average cost to produce a single item? They divide their total cost function by their total production function! ➗ In this tutorial, you'll learn how to perform division, one of the four basic operations on functio...

TermDefinitionExample Quotient of FunctionsA new function created by dividing one function, f(x), by another function, g(x). It is denoted as (f/g)(x).If f(x) = 10x and g(x) = 2, then (f/g)(x) = 10x / 2 = 5x. DomainThe set of all possible input values (x-values) for which a function is defined.The domain of f(x) = √x is all non-negative real numbers, or [0, ∞). Domain of a Quotient FunctionThe set of all x-values that are in the domain of BOTH the numerator function and the denominator function, with the additional rule that any x-value making the denominator function equal to zero must be excluded.For (f/g)(x) where f(x) = x and g(x) = x-4, the domain is all real numbers except x=4, because x=4 would make the denominator zero. Rational FunctionA function that can be written as the ratio...

The Quotient Function Formula \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} This is the fundamental definition for dividing two functions, f(x) and g(x). To find the new function, you place the first function in the numerator and the second function in the denominator. The Domain of a Quotient Function Rule Domain of \left(\frac{f}{g}\right) = \{x \in D_f \cap D_g \mid g(x) \neq 0\} This rule states that the domain of the quotient function (f/g) is the intersection (overlap) of the domains of f (D_f) and g (D_g), excluding any x-values for which the denominator function g(x) equals zero.