Explanation Procedure used: Formula for an inverse Function: “If a function f is one-to-one, a formula for its inverse can generally be found as follows, 1. Replace f ( x ) with y . 2. Interchange x and y . 3. Solve for y . 4. Replace y with f − 1 ( x ) . Calculation: Given that, the function is f ( x ) = 1 x − 4 . Replace y for f ( x ) in f ( x ) = 1 x − 4 , y = 1 x − 4 Change the variable x for y and y for x in y = 1 x − 4 . x = 1 y − 4 x ( y − 4 ) = 1 x y − 4 x = 1 x y = 4 x + 1 y = 4 x + 1 x Simplify the terms to obtain the value of y , y = 4 x + 1 x . Change f − 1 ( x ) for y in y = 4 x + 1 x to get the inverse of the function as, f − 1 ( x ) = 4 x + 1 x . Therefore, the inverse function of f is f − 1 ( x ) = 4 x + 1 x . Here, the both functions are f ( x ) = 1 x − 4 and f − 1 ( x ) = 4 x + 1 x . The denominator of f ( x ) = 1 x − 4 is x − 4 , so the function f ( x ) = 1 x − 4 is undefined at x = 4 . Thus, the domain of the function f ( x ) = 1 x − 4 is set of all real numbers except x = 4 . The function x = 4 approaches − ∞ as x approaches 4 from left and the function approaches ∞ as x approaches 4 from right. The function f ( x ) = 1 x − 4 approaches zero whenever the value of x approaches infinity. Thus, the range of the function f ( x ) = 1 x − 4 is ( − ∞ , 0 ) ∪ ( 0 , ∞ )

6th Edition

ISBN: 2810000027802

Author: BITTINGER

Publisher: PEARSON

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Chapter 5, Problem 9T

To determine

The inverse of one-to-one function f(x)=1x−4. Give the domain and range of function and its inverse. Sketch the graph of both functions on same screen.

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Chapter 5, Problem 8T

Chapter 5, Problem 10T

Chapter 5 Solutions

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Ch. 5.1 - Find the inverse of the relation. {(7, 8), (2, 8),...Ch. 5.1 - Find the inverse of the relation. {(0, 1), (5, 6),...Ch. 5.1 - Find the inverse of the relation. {(1, 1), (3, 4)}Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Graph the equation by substituting and plotting...Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Given the function g, prove that g is not...Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Using the horizontal-line test, determine whether...Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Graph the function and its inverse using a...Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Graph the function and determine whether the...Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.1 - Prob. 59E Ch. 5.1 - Prob. 60E Ch. 5.1 - Prob. 61E Ch. 5.1 - Prob. 62E Ch. 5.1 - Prob. 63E Ch. 5.1 - Prob. 64E Ch. 5.1 - Prob. 65E Ch. 5.1 - Prob. 66E Ch. 5.1 - Prob. 67E Ch. 5.1 - Prob. 68E Ch. 5.1 - Prob. 69E Ch. 5.1 - Prob. 70E Ch. 5.1 - Prob. 71E Ch. 5.1 - Prob. 72E Ch. 5.1 - Prob. 73E Ch. 5.1 - Prob. 74E Ch. 5.1 - Prob. 75E Ch. 5.1 - Prob. 76E Ch. 5.1 - Prob. 77E Ch. 5.1 - Prob. 78E Ch. 5.1 - Prob. 79E Ch. 5.1 - Prob. 80E Ch. 5.1 - Prob. 81E Ch. 5.1 - Prob. 82E Ch. 5.1 - Prob. 83E Ch. 5.1 - Prob. 84E Ch. 5.1 - Prob. 85E Ch. 5.1 - Prob. 86E Ch. 5.1 - Prob. 87E Ch. 5.1 - Prob. 88E Ch. 5.1 - Prob. 89E Ch. 5.1 - Prob. 90E Ch. 5.1 - Prob. 91E Ch. 5.1 - Prob. 92E Ch. 5.1 - Prob. 93E Ch. 5.1 - Prob. 94E Ch. 5.1 - Prob. 95E Ch. 5.1 - Prob. 96E Ch. 5.1 - Prob. 97E Ch. 5.1 - Prob. 98E Ch. 5.1 - Prob. 99E Ch. 5.1 - Prob. 100E Ch. 5.1 - Prob. 101E Ch. 5.1 - Prob. 102E Ch. 5.1 - Prob. 103E Ch. 5.1 - Prob. 104E Ch. 5.1 - Prob. 105E Ch. 5.1 - Prob. 106E Ch. 5.1 - Prob. 107E Ch. 5.1 - Prob. 108E Ch. 5.1 - Prob. 109E Ch. 5.1 - Prob. 110E Ch. 5.1 - Prob. 111E Ch. 5.1 - Prob. 112E Ch. 5.1 - Prob. 113E Ch. 5.1 - Given the function f(x) = ax + b, a 0, find the...Ch. 5.2 - Find each of the following, to four decimal...Ch. 5.2 - Find each of the following, to four decimal...Ch. 5.2 - Find each of the following, to four decimal...Ch. 5.2 - Find each of the following, to four decimal...Ch. 5.2 - In Exercises 510, match the function with one of...Ch. 5.2 - In Exercises 510, match the function with one of...Ch. 5.2 - In Exercises 510, match the function with one of...Ch. 5.2 - In Exercises 510, match the function with one of...Ch. 5.2 - In Exercises 510, match the function with one of...Ch. 5.2 - In Exercises 510, match the function with one of...Ch. 5.2 - Graph the function by substituting and plotting...Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Graph the function by substituting and plotting...Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - Prob. 25E Ch. 5.2 - Prob. 26E Ch. 5.2 - Prob. 27E Ch. 5.2 - Prob. 28E Ch. 5.2 - Prob. 29E Ch. 5.2 - Prob. 30E Ch. 5.2 - Prob. 31E Ch. 5.2 - Prob. 32E Ch. 5.2 - Prob. 33E Ch. 5.2 - Prob. 34E Ch. 5.2 - Prob. 35E Ch. 5.2 - Prob. 36E Ch. 5.2 - Sketch the graph of the function and check the...Ch. 5.2 - Prob. 38E Ch. 5.2 - Prob. 39E Ch. 5.2 - Prob. 40E Ch. 5.2 - Prob. 41E Ch. 5.2 - Prob. 42E Ch. 5.2 - Prob. 43E Ch. 5.2 - Prob. 44E Ch. 5.2 - Prob. 45E Ch. 5.2 - Prob. 46E Ch. 5.2 - Prob. 47E Ch. 5.2 - Prob. 48E Ch. 5.2 - Prob. 49E Ch. 5.2 - Prob. 50E Ch. 5.2 - Compound Interest. Suppose that 82,000 is invested...Ch. 5.2 - Compound Interest. Suppose that 750 is invested at...Ch. 5.2 - Interest on a CD. 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Then...Ch. 5.5 - Prob. 12E Ch. 5.5 - Prob. 13E Ch. 5.5 - Prob. 14E Ch. 5.5 - Prob. 15E Ch. 5.5 - Prob. 16E Ch. 5.5 - Prob. 17E Ch. 5.5 - Prob. 18E Ch. 5.5 - Prob. 19E Ch. 5.5 - Prob. 20E Ch. 5.5 - Prob. 21E Ch. 5.5 - Prob. 22E Ch. 5.5 - Prob. 23E Ch. 5.5 - Prob. 24E Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - Prob. 28E Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Prob. 31E Ch. 5.5 - Prob. 32E Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Solve the logarithmic equation algebraically. Then...Ch. 5.5 - Prob. 36E Ch. 5.5 - Prob. 37E Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5.5 - Prob. 43E Ch. 5.5 - Prob. 44E Ch. 5.5 - Prob. 45E Ch. 5.5 - Prob. 46E Ch. 5.5 - Prob. 47E Ch. 5.5 - Prob. 48E Ch. 5.5 - Prob. 49E Ch. 5.5 - Prob. 50E Ch. 5.5 - Prob. 51E Ch. 5.5 - Prob. 52E Ch. 5.5 - Prob. 53E Ch. 5.5 - Prob. 54E Ch. 5.5 - Prob. 55E Ch. 5.5 - Prob. 56E Ch. 5.5 - Prob. 57E Ch. 5.5 - Prob. 58E Ch. 5.5 - Prob. 59E Ch. 5.5 - Prob. 60E Ch. 5.5 - Prob. 61E Ch. 5.5 - Prob. 62E Ch. 5.5 - Prob. 63E Ch. 5.5 - Prob. 64E Ch. 5.5 - Prob. 65E Ch. 5.5 - Prob. 66E Ch. 5.5 - Prob. 67E Ch. 5.5 - Prob. 68E Ch. 5.5 - Prob. 69E Ch. 5.5 - Prob. 70E Ch. 5.5 - Prob. 71E Ch. 5.5 - Prob. 72E Ch. 5.5 - Prob. 73E Ch. 5.5 - Prob. 74E Ch. 5.5 - Prob. 75E Ch. 5.5 - Prob. 76E Ch. 5.5 - Prob. 77E Ch. 5.5 - Prob. 78E Ch. 5.5 - Prob. 79E Ch. 5.5 - Prob. 80E Ch. 5.5 - Prob. 81E Ch. 5.5 - Prob. 82E Ch. 5.5 - Prob. 83E Ch. 5.5 - Prob. 84E Ch. 5.5 - Prob. 85E Ch. 5.5 - Prob. 86E Ch. 5.5 - Prob. 87E Ch. 5.5 - Prob. 88E Ch. 5.5 - Prob. 89E Ch. 5.5 - Prob. 90E Ch. 5.5 - Prob. 91E Ch. 5.5 - Prob. 92E Ch. 5.5 - Prob. 93E Ch. 5.5 - Prob. 94E Ch. 5.5 - Prob. 95E Ch. 5.5 - Prob. 96E Ch. 5.6 - Population Growth of Raleigh. Raleigh, North...Ch. 5.6 - Prob. 2E Ch. 5.6 - Prob. 3E Ch. 5.6 - Prob. 4E Ch. 5.6 - Prob. 5E Ch. 5.6 - Georgia OKeeffe Painting. On November 20, 2014,...Ch. 5.6 - Prob. 7E Ch. 5.6 - Prob. 8E Ch. 5.6 - Carbon Dating. In 1970, Amos Flora of Flora,...Ch. 5.6 - Prob. 10E Ch. 5.6 - Prob. 11E Ch. 5.6 - Prob. 12E Ch. 5.6 - Prob. 13E Ch. 5.6 - Prob. 14E Ch. 5.6 - Prob. 15E Ch. 5.6 - Oil Consumption. In 1980, China consumed 1.85...Ch. 5.6 - Prob. 17E Ch. 5.6 - Prob. 18E Ch. 5.6 - Prob. 19E Ch. 5.6 - Prob. 20E Ch. 5.6 - Prob. 21E Ch. 5.6 - Prob. 22E Ch. 5.6 - Prob. 23E Ch. 5.6 - Prob. 24E Ch. 5.6 - Prob. 25E Ch. 5.6 - Prob. 26E Ch. 5.6 - Prob. 27E Ch. 5.6 - Prob. 28E Ch. 5.6 - Prob. 29E Ch. 5.6 - Prob. 30E Ch. 5.6 - Prob. 31E Ch. 5.6 - Prob. 32E Ch. 5.6 - Prob. 33E Ch. 5.6 - Prob. 34E Ch. 5.6 - Prob. 35E Ch. 5.6 - Prob. 36E Ch. 5.6 - Prob. 37E Ch. 5.6 - Prob. 38E Ch. 5.6 - Prob. 39E Ch. 5.6 - Prob. 40E Ch. 5.6 - Prob. 41E Ch. 5.6 - Prob. 42E Ch. 5.6 - Prob. 43E Ch. 5.6 - Prob. 44E Ch. 5.6 - Prob. 45E Ch. 5.6 - Prob. 46E Ch. 5.6 - Prob. 47E Ch. 5 - Determine whether the statement is true or false....Ch. 5 - Prob. 2MC Ch. 5 - Prob. 3MC Ch. 5 - Prob. 4MC Ch. 5 - Prob. 5MC Ch. 5 - Prob. 6MC Ch. 5 - Prob. 7MC Ch. 5 - Prob. 8MC Ch. 5 - Prob. 9MC Ch. 5 - Prob. 10MC Ch. 5 - Prob. 11MC Ch. 5 - Prob. 12MC Ch. 5 - Prob. 13MC Ch. 5 - Prob. 14MC Ch. 5 - Prob. 15MC Ch. 5 - Prob. 16MC Ch. 5 - Prob. 17MC Ch. 5 - Prob. 18MC Ch. 5 - Prob. 19MC Ch. 5 - Prob. 20MC Ch. 5 - Prob. 21MC Ch. 5 - Prob. 22MC Ch. 5 - Prob. 23MC Ch. 5 - Prob. 24MC Ch. 5 - Prob. 25MC Ch. 5 - Prob. 26MC Ch. 5 - Prob. 27MC Ch. 5 - Prob. 28MC Ch. 5 - Prob. 29MC Ch. 5 - Prob. 30MC Ch. 5 - Prob. 31MC Ch. 5 - Prob. 1RE Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - Prob. 6RE Ch. 5 - Prob. 7RE Ch. 5 - Prob. 8RE Ch. 5 - Prob. 9RE Ch. 5 - Prob. 10RE Ch. 5 - Prob. 11RE Ch. 5 - Prob. 12RE Ch. 5 - Prob. 13RE Ch. 5 - Prob. 14RE Ch. 5 - Prob. 15RE Ch. 5 - Prob. 16RE Ch. 5 - Prob. 17RE Ch. 5 - Prob. 18RE Ch. 5 - Prob. 19RE Ch. 5 - Prob. 20RE Ch. 5 - Prob. 21RE Ch. 5 - Prob. 22RE Ch. 5 - Prob. 23RE Ch. 5 - Prob. 24RE Ch. 5 - Prob. 25RE Ch. 5 - Prob. 26RE Ch. 5 - Prob. 27RE Ch. 5 - Prob. 28RE Ch. 5 - Prob. 29RE Ch. 5 - Prob. 30RE Ch. 5 - Prob. 31RE Ch. 5 - Prob. 32RE Ch. 5 - In Exercises 3136, match the equation with one of...Ch. 5 - Prob. 34RE Ch. 5 - Prob. 35RE Ch. 5 - Prob. 36RE Ch. 5 - Prob. 37RE Ch. 5 - Prob. 38RE Ch. 5 - Prob. 39RE Ch. 5 - Prob. 40RE Ch. 5 - Prob. 41RE Ch. 5 - Prob. 42RE Ch. 5 - Prob. 43RE Ch. 5 - Prob. 44RE Ch. 5 - Prob. 45RE Ch. 5 - Prob. 46RE Ch. 5 - Prob. 47RE Ch. 5 - Prob. 48RE Ch. 5 - Prob. 49RE Ch. 5 - Prob. 50RE Ch. 5 - Prob. 51RE Ch. 5 - Prob. 52RE Ch. 5 - Prob. 53RE Ch. 5 - Prob. 54RE Ch. 5 - Prob. 55RE Ch. 5 - Prob. 56RE Ch. 5 - Prob. 57RE Ch. 5 - Prob. 58RE Ch. 5 - Prob. 59RE Ch. 5 - Prob. 60RE Ch. 5 - Prob. 61RE Ch. 5 - Prob. 62RE Ch. 5 - Prob. 63RE Ch. 5 - Prob. 64RE Ch. 5 - Prob. 65RE Ch. 5 - Prob. 66RE Ch. 5 - Prob. 67RE Ch. 5 - Prob. 68RE Ch. 5 - Prob. 69RE Ch. 5 - Prob. 70RE Ch. 5 - Prob. 71RE Ch. 5 - Prob. 72RE Ch. 5 - Prob. 73RE Ch. 5 - Prob. 74RE Ch. 5 - Prob. 75RE Ch. 5 - Prob. 76RE Ch. 5 - Prob. 77RE Ch. 5 - Prob. 78RE Ch. 5 - Prob. 79RE Ch. 5 - Prob. 80RE Ch. 5 - Prob. 81RE Ch. 5 - Prob. 82RE Ch. 5 - Prob. 83RE Ch. 5 - Prob. 84RE Ch. 5 - Prob. 85RE Ch. 5 - Prob. 86RE Ch. 5 - Prob. 87RE Ch. 5 - Prob. 88RE Ch. 5 - Prob. 89RE Ch. 5 - Prob. 90RE Ch. 5 - Prob. 91RE Ch. 5 - Prob. 92RE Ch. 5 - Prob. 93RE Ch. 5 - Prob. 94RE Ch. 5 - Prob. 95RE Ch. 5 - Prob. 96RE Ch. 5 - Prob. 97RE Ch. 5 - Prob. 98RE Ch. 5 - Prob. 99RE Ch. 5 - Prob. 100RE Ch. 5 - Prob. 1T Ch. 5 - Prob. 2T Ch. 5 - Prob. 3T Ch. 5 - Prob. 4T Ch. 5 - Prob. 5T Ch. 5 - Prob. 6T Ch. 5 - Prob. 7T Ch. 5 - Prob. 8T Ch. 5 - Prob. 9T Ch. 5 - Prob. 10T Ch. 5 - Prob. 11T Ch. 5 - Prob. 12T Ch. 5 - Prob. 13T Ch. 5 - Prob. 14T Ch. 5 - Prob. 15T Ch. 5 - Prob. 16T Ch. 5 - Prob. 17T Ch. 5 - Prob. 18T Ch. 5 - Prob. 19T Ch. 5 - Prob. 20T Ch. 5 - Prob. 21T Ch. 5 - Prob. 22T Ch. 5 - Prob. 23T Ch. 5 - Prob. 24T Ch. 5 - Prob. 25T Ch. 5 - Prob. 26T Ch. 5 - Prob. 27T Ch. 5 - Prob. 28T Ch. 5 - Prob. 29T Ch. 5 - Prob. 30T Ch. 5 - Earthquake Magnitude. The Tohoku earthquake near...Ch. 5 - Prob. 32T Ch. 5 - Compound Interest. Suppose that 1000 is invested...Ch. 5 - Prob. 34T Ch. 5 - Prob. 35T

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The inverse of one-to-one function f ( x ) = 1 x − 4 . Give the domain and range of function and its inverse. Sketch the graph of both functions on same screen.

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The inverse of one-to-one function f(x)=1x−4. Give the domain and range of function and its inverse. Sketch the graph of both functions on same screen.

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Chapter 5 Solutions