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DISCUSS:Solving an Equation for an Unknown FunctionIn Exercises 6972 of Section 2.7 you
Chapter 2, Problem 105(choose chapter or problem)
DISCUSS:Solving an Equation for an Unknown FunctionIn Exercises 6972 of Section 2.7 you were asked to solveequations in which the unknowns are functions. Now thatwe know about inverses and the identity function (see Exercise104), we can use algebra to solve such equations. Forinstance, to solve f g h for the unknown function f, weperform the following steps:f g h Problem: Solve for ff g g1 h g1 Compose with g1 on the rightf I h g1 Because g g1 5 If h g1 Because f I 5 f So the solution is f h g1. Use this technique to solvethe equation f g h for the indicated unknown function.(a) Solve for f, where g1x2 2x 1 andh1x2 4x2 4x 7.(b) Solve for g, where f1x2 3x 5 andh1x2 3x2 3x 2.
Questions & Answers
QUESTION:
DISCUSS:Solving an Equation for an Unknown FunctionIn Exercises 6972 of Section 2.7 you were asked to solveequations in which the unknowns are functions. Now thatwe know about inverses and the identity function (see Exercise104), we can use algebra to solve such equations. Forinstance, to solve f g h for the unknown function f, weperform the following steps:f g h Problem: Solve for ff g g1 h g1 Compose with g1 on the rightf I h g1 Because g g1 5 If h g1 Because f I 5 f So the solution is f h g1. Use this technique to solvethe equation f g h for the indicated unknown function.(a) Solve for f, where g1x2 2x 1 andh1x2 4x2 4x 7.(b) Solve for g, where f1x2 3x 5 andh1x2 3x2 3x 2.
ANSWER:Problem 105
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 
So the solution is 
the equation
(a) Solve for f, where 
(b) Solve for g, where 
Step by Step Solution
Step 1 of 3
The expression for the unknown function when two function is given,