Ebook College algebra (9th edition): Part 2
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Ebook College algebra (9th edition): Part 2
Exponential andLogarithmic FunctionsOutline6.1Composite Functions6.6Logarithmic and Exponential6.9Building Exponential, logarithmic.6JOne to One funct Ebook College algebra (9th edition): Part 2 tions; InverseEquationsand Logistic Models from DataFunctions6.7Financial .Models•Chapter Review6.3Exponential functions6.8Exponential Growth and Decay•Chapter lest6.4logarithmic FunctionsModels; Newtons law; Logistic•Cumulative Review65Properties of LogarithmsGrowth and Decay Models•Chapter Project Ebook College algebra (9th edition): Part 2 sDepreciation of CarsYou are ready to buy that first new car. You know that cars lose value over lime due to depreciation and that different ears haveEbook College algebra (9th edition): Part 2
different rates of depreciation. So you will research the depreciation rates for the cars you arc thinking of buying. After all. the lower the deprecExponential andLogarithmic FunctionsOutline6.1Composite Functions6.6Logarithmic and Exponential6.9Building Exponential, logarithmic.6JOne to One funct Ebook College algebra (9th edition): Part 2 oncentrated on polynomial and rational functions. These functions belong to the class of algebraic functions, tfiat is. functions that can be expressed in terms o‘ sums, differences, products, quotients, powers, or roots of polynomials. Functions that are not algebraic are termed transcendental (the Ebook College algebra (9th edition): Part 2 y transcend, or go heyond, algebraic functions).A Look Ahead > In Ulis chapter, we study two transcendental functions: the exponential function and thEbook College algebra (9th edition): Part 2
e 'egarithme function These funcrons occur frequently in a wide variety of applications, such as belogy, chemistry, economics, and psychology.The chapExponential andLogarithmic FunctionsOutline6.1Composite Functions6.6Logarithmic and Exponential6.9Building Exponential, logarithmic.6JOne to One funct Ebook College algebra (9th edition): Part 2 mic functions.400SEChttps://khothuvien.cori!6.1 Composite FunctionsPreparing for this section Before getting started, review the following:• Find the Value of a Function (Section 3.1. pp. 203-206)• Domain of a Function (Section 3.1. pp. 2O6-2OX)Now Work the 'Are You Prepared?' problems on page 406.O Ebook College algebra (9th edition): Part 2 BJECTIVES 1 Form a Composite Function (p. 401)2 Find the Domain of a Composite Function (p. 402)Figure 1DEFINITION1 Form a Composite FunctionSuppose tEbook College algebra (9th edition): Part 2
hat an oil tanker is leaking oil and you want to determine the area of the circular oil patch around the ship. See Figure 1. It is determined that theExponential andLogarithmic FunctionsOutline6.1Composite Functions6.6Logarithmic and Exponential6.9Building Exponential, logarithmic.6JOne to One funct Ebook College algebra (9th edition): Part 2 e. Therefore. the radius r of the oil patch at any time f. in minutes, is given by r(t) 3f. So after 20 minutes the radius of the oil patch is r(20) = 3(20) = 60 feel.lhe area A of a circle as a function of the radius r is given by zl(r) irr*. Hie area of the circular patch of oil after 20 minutes i Ebook College algebra (9th edition): Part 2 s .4(60) = ir(60)2 = 3600.7 square feet. Notice that 60 r(20). so 4(60)4(r(20)). lhe argument of the function Ais the output a function!In general, weEbook College algebra (9th edition): Part 2
can find the area of the oil patch as a function of lime t by evaluating A{r(t)) and obtaining 4(r(f))4(3r)-(3f)7 Vjrr’.’lhe function4(r(z)) is a speExponential andLogarithmic FunctionsOutline6.1Composite Functions6.6Logarithmic and Exponential6.9Building Exponential, logarithmic.6JOne to One funct Ebook College algebra (9th edition): Part 2 3. then, by a substitution process. we can obtain the original function: y f(u) f(g(x))(2a I 3)7.In general, suppose that f and g are two functions and that X is a number in the domain of g. Ry evaluating g al X, we gel g(x). If g(x) is in the domain of f. then we may evaluate f at g(x) and obtain t Ebook College algebra (9th edition): Part 2 he expression /(g(x)). Hie correspondence from X to /(g(x)) is called a composite function f » g.Given two functions f and g. the composite function,Ebook College algebra (9th edition): Part 2
denoted by f V g (read as"/ composed with g"). is defined by(/ “ g)(x) = /(g(x))lhe domain of f » g is the set of all numbers-V in the domain of g sucExponential andLogarithmic FunctionsOutline6.1Composite Functions6.6Logarithmic and Exponential6.9Building Exponential, logarithmic.6JOne to One functExponential andLogarithmic FunctionsOutline6.1Composite Functions6.6Logarithmic and Exponential6.9Building Exponential, logarithmic.6JOne to One functGọi ngay
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