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AlgebraQ&A Library105. 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 = fStart your trial now! First week only $4.99!*arrow_forward*

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:

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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