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

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
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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