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6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

Chapter 1.5, Problem 138E

Textbook Problem

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Proof Prove that if *f* has an inverse function, then

To determine

If f has an inverse function, then ( f − 1 ) − 1 = f .

**Given:**

**Explanation:**

Use the definition of an inverse is the inverse of (f o g).

Therefore,

Example:

Calculus: Early Transcendental Functions (MindTap Course List)

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Numerical and Graphical Analysis In Exercises 87...Ch. 1.5 - Numerical and Graphical Analysis In Exercises 87...Ch. 1.5 - Missing Coordinates Determine the missing...Ch. 1.5 - HOW DO YOU SEE IT? You use a graphing utility to...Ch. 1.5 - Sketching a Graph In Exercises 91-94, sketch the...Ch. 1.5 - Sketching a Graph Sketching a Graph In Exercises...Ch. 1.5 - Sketching a Graph In Exercises 91-94, sketch the...Ch. 1.5 - Sketching a Graph In Exercises 91-94, sketch the...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Using Properties In Exercises 107 and 108, use the...Ch. 1.5 - Using Properties In Exercises 99 and 100, use the...Ch. 1.5 - EXPLORING CONCEPTS Inverse Trigonometric Functions...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Point of Intersection In Exercises 121 and 122,...Ch. 1.5 - Point of Intersection In Exercises 121 and 122,...Ch. 1.5 - Inverse Functions Describe how to find the inverse...Ch. 1.5 - Describing RelationshipsDescribe the relationship...Ch. 1.5 - Inverse Trigonometric Functions and...Ch. 1.5 - Fill in the Blank In Exercises 133 and 134, fill...Ch. 1.5 - Fill in the Blank In Exercises 133 and 134, fill...Ch. 1.5 - Verifying an Identity In Exercises 135 and 136,...Ch. 1.5 - Verifying an Identity In Exercises 135 and 136,...Ch. 1.5 - Verifying an Identity Verify each identity. (a)...Ch. 1.5 - Using an Identity Use the results of Exercise 137...Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - arcsin2x+arccos2x=1Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - True or False? 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Inverse Functions In Exercises 73-76, illustrate...Ch. 1.6 - Inverse Functions In Exercises 73-76, illustrate...Ch. 1.6 - Finding Inverse Functions In Exercises 77-80, (a)...Ch. 1.6 - Finding Inverse Functions In Exercises 77-80, (a)...Ch. 1.6 - Finding Inverse Functions In Exercises 77-80, (a)...Ch. 1.6 - Finding Inverse Functions In Exercises 77-80, (a)...Ch. 1.6 - Applying Inverse Properties In Exercises 81-86,...Ch. 1.6 - Applying Inverse Properties In Exercises 8186,...Ch. 1.6 - Applying Inverse Properties In Exercises 81-86,...Ch. 1.6 - Applying Inverse Properties In Exercises 81-86,...Ch. 1.6 - Applying Inverse Properties In Exercises 81-86,...Ch. 1.6 - Applying Inverse Properties In Exercises 81-86,...Ch. 1.6 - Using Properties of Logarithms In Exercises 87 and...Ch. 1.6 - Using Properties of Logarithms In Exercises 87 and...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Expanding a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Condensing a Logarithmic Expression In Exercises...Ch. 1.6 - Solving an Exponential or Logarithmic Equation...Ch. 1.6 - Solving an Exponential or Logarithmic Equation...Ch. 1.6 - Solving an Exponential or Logarithmic Equation...Ch. 1.6 - Solving an Exponential or Logarithmic Equation In...Ch. 1.6 - Solving an Inequality In Exercises 111114, solve...Ch. 1.6 - Solving an Inequality In Exercises 119-122, solve...Ch. 1.6 - Solving an Inequality In Exercises 119-122, solve...Ch. 1.6 - Solving an Inequality In Exercises 111114, solve...Ch. 1.6 - Solving an Inequality In Exercises 115 and 116,...Ch. 1.6 - Solving an Exponential or Logarithmic Equation In...Ch. 1.6 - Stating PropertiesIn your own words, stale the...Ch. 1.6 - Think About It Explain why In ex= x.Ch. 1.6 - Stating PropertiesIn your own words, stale the...Ch. 1.6 - Describe the Relationship Describe the...Ch. 1.6 - Analyze a Statement The table of values below was...Ch. 1.6 - HOW DO YOU SEE IT? 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In Exercises 125 and 126, determine...Ch. 1.6 - Comparing Functions Use a graphing utility to...Ch. 1.6 - Comparing Functions Use a graphing utility to...Ch. 1.6 - Analyzing a Function Let f(x)=ln(x+x2+1) (a) Use a...Ch. 1.6 - Prime Number TheoremThere are 25 prime numbers...Ch. 1.6 - In Exercises 135 and 136, find the exact value of...Ch. 1.6 - In Exercises 135 and 136, find the exact value of...Ch. 1.6 - Proof Prove that ln(x/y)=lnxlny,x0,y0.Ch. 1.6 - Proof Prove that lnxy=ylnx.Ch. 1 - Finding Intercepts In Exercises 1-4, find any...Ch. 1 - Finding Intercepts In Exercises 1-4, find any...Ch. 1 - Finding Intercepts In Exercises 1-4, find any...Ch. 1 - Finding Intercepts In Exercises 1-4, find any...Ch. 1 - Testing for Symmetry In Exercises 5-8, test for...Ch. 1 - Testing for Symmetry In Exercises 5-8, test for...Ch. 1 - Testing for Symmetry In Exercises 5-8, test for...Ch. 1 - Testing for Symmetry In Exercises 5-8, test for...Ch. 1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. 1 - 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Using the Vertical Line Test In Exercises 45 and...Ch. 1 - Using the Vertical Line Test In Exercises 4346,...Ch. 1 - Deciding Whether an Equation Is a Function In...Ch. 1 - Transformations of Functions Use a graphing...Ch. 1 - Conjecture (a) Use a graphing utility to graph the...Ch. 1 - Think About It Use the results of Exercise 48 to...Ch. 1 - Think About It What is the minimum degree of the...Ch. 1 - Writing The following graphs give the profits P...Ch. 1 - Area A wire 24 inches long is to be cut into four...Ch. 1 - Stress Test Amachine pan was tested by bending it...Ch. 1 - Median IncomeThe data in thetable show the median...Ch. 1 - Summer Olympics The table lists the U.S. media...Ch. 1 - Harmonic MotionThe motion of an oscillating weight...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Sketching a Graph In Exercises 105 and 106, sketch...Ch. 1 - Sketching a Graph In Exercises 105 and 106, sketch...Ch. 1 - Evaluating Trigonometric Functions In Exercises...Ch. 1 - Evaluating Trigonometric Functions In Exercises...Ch. 1 - Sketching the Graph of an Exponential Function In...Ch. 1 - Sketching the Graph of an Exponential Function In...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Sketching the Graph of a Logarithmic Function In...Ch. 1 - Sketching the Graph of a Logarithmic Function In...Ch. 1 - Expanding a Logarithmic Expression In Exercises...Ch. 1 - Expanding a Logarithmic Expression In Exercises...Ch. 1 - Condensing a Logarithmic Expression In Exercises...Ch. 1 - Condensing a Logarithmic Expression In Exercises...Ch. 1 - Solving an EquationIn Exercises 77 and 78, solve...Ch. 1 - Solving an Exponential or Logarithmic Equation In...Ch. 1 - Finding Inverse Functions In Exercises 79 and 80,...Ch. 1 - Finding Inverse Functions In Exercises 79 and 80,...Ch. 1 - Finding Tangent Lines Consider the circle...Ch. 1 - Finding Tangent Lines There are two tangent lines...Ch. 1 - Heaviside Function The Heaviside function H(x) is...Ch. 1 - Sketching Transformations Consider the graph of...Ch. 1 - Maximum Area A rancher plans to fence a...Ch. 1 - Maximum Area A rancher has 300 feet of fencing to...Ch. 1 - Writing a Function You are in a boat 2 miles from...Ch. 1 - Analyzing a Function Graph the function f(x)=e2ex...Ch. 1 - Slope of a Tangent Line One of the fundamental...Ch. 1 - Slope of a Tangent Line Sketch the graph of the...Ch. 1 - Composite Functions Let f(x)=11x. (a) What are the...Ch. 1 - Graphing an Equation Explain how you would graph...Ch. 1 - Sound Intensity A Large room contains two speakers...Ch. 1 - Sound Intensity Suppose the speakers in Exercise...Ch. 1 - Lemniscate Let d1 and d2 be the distances from the...

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