Homework Help is Here – Start Your Trial Now!
Math
Algebra
105. DISCUSS: Solving an Equation for an Unknown Function In Exercises 69-72 of Section 2.7 you were asked to solve equations in which the unknowns are functions. Now that we know about inverses and the identity function (see Exer- cise 104), we can use algebra to solve such equations. For instance, to solve f• g = h for the unknown function f, we perform the following steps: So the solution is f = h °g. Use this technique to solve the equation f°g = h for the indicated unknown function. (a) Solve for f, where g(x) = 2x + 1 and h(x) = 4x² + 4x + 7. (b) Solve for g, where f(x) = 3x + 5 and h(x) = 3x + 3x + 2. f°g = h f•g•g! = h°g* fol = h°g! f = h°g" Problem: Solve for f Compose with g on the right Because gog" =| Because fl= f

105. DISCUSS: Solving an Equation for an Unknown Function In Exercises 69-72 of Section 2.7 you were asked to solve equations in which the unknowns are functions. Now that we know about inverses and the identity function (see Exer- cise 104), we can use algebra to solve such equations. For instance, to solve f• g = h for the unknown function f, we perform the following steps: So the solution is f = h °g. Use this technique to solve the equation f°g = h for the indicated unknown function. (a) Solve for f, where g(x) = 2x + 1 and h(x) = 4x² + 4x + 7. (b) Solve for g, where f(x) = 3x + 5 and h(x) = 3x + 3x + 2. f°g = h f•g•g! = h°g* fol = h°g! f = h°g" Problem: Solve for f Compose with g on the right Because gog" =| Because fl= f

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.8: One-to-one Functions And Their Inverses
Problem 105E
See similar textbooks
icon
Related questions
Question

5. DISCUSS: Solving an Equation for an Unknown Function
In Exercises 69–72 of Section 2.7 you were asked to solve
equations in which the unknowns are functions. Now that
we know about inverses and the identity function (see Exercise 104), we can use algebra to solve such equations. For
instance, to solve f  g  h for the unknown function f, we
perform the following steps:

105. DISCUSS: Solving an Equation for an Unknown Function In Exercises 69-72 of Section 2.7 you were asked to solve equations in which the unknowns are functions. Now that we know about inverses and the identity function (see Exer- cise 104), we can use algebra to solve such equations. For instance, to solve f• g = h for the unknown function f, we perform the following steps: So the solution is f = h °g. Use this technique to solve the equation f°g = h for the indicated unknown function. (a) Solve for f, where g(x) = 2x + 1 and h(x) = 4x² + 4x + 7. (b) Solve for g, where f(x) = 3x + 5 and h(x) = 3x + 3x + 2. f°g = h f•g•g! = h°g* fol = h°g! f = h°g" Problem: Solve for f Compose with g on the right Because gog" =| Because fl= f
Transcribed Image Text:105. DISCUSS: Solving an Equation for an Unknown Function In Exercises 69-72 of Section 2.7 you were asked to solve equations in which the unknowns are functions. Now that we know about inverses and the identity function (see Exer- cise 104), we can use algebra to solve such equations. For instance, to solve f• g = h for the unknown function f, we perform the following steps: So the solution is f = h °g. Use this technique to solve the equation f°g = h for the indicated unknown function. (a) Solve for f, where g(x) = 2x + 1 and h(x) = 4x² + 4x + 7. (b) Solve for g, where f(x) = 3x + 5 and h(x) = 3x + 3x + 2. f°g = h f•g•g! = h°g* fol = h°g! f = h°g" Problem: Solve for f Compose with g on the right Because gog" =| Because fl= f
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS