In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y = f(x) to represent a function, an applied problem might use C = C(q) to represent the cost C of manufacturing q units of a good since, in economics, q is used for output. Because of this, the inverse notation f used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C = C(q) will be q = q(C). So C = C(g) is a function that represents the cost C as a function of the output q, while q = q(C) is a function that represents the output q as a function of the cost C. Income Taxes The function T(g) = 1670 + 0.15(g – 16,700) represents the 2009 federal income tax T (in dollars) due for a “married filing jointly" filer whose modified adjusted gross income is g dollars, where 16,700 s g s 67,900. (a) What is the domain of the function T? (b) Given that the tax due T is an increasing linear function of modified adjusted gross income g, find the range of the function T. (c) Find adjusted gross income g as a function of federal income tax T. What are the domain and the range of this function?
In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y = f(x) to represent a function, an applied problem might use C = C(q) to represent the cost C of manufacturing q units of a good since, in economics, q is used for output. Because of this, the inverse notation f used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C = C(q) will be q = q(C). So C = C(g) is a function that represents the cost C as a function of the output q, while q = q(C) is a function that represents the output q as a function of the cost C. Income Taxes The function T(g) = 1670 + 0.15(g – 16,700) represents the 2009 federal income tax T (in dollars) due for a “married filing jointly" filer whose modified adjusted gross income is g dollars, where 16,700 s g s 67,900. (a) What is the domain of the function T? (b) Given that the tax due T is an increasing linear function of modified adjusted gross income g, find the range of the function T. (c) Find adjusted gross income g as a function of federal income tax T. What are the domain and the range of this function?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 55E
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