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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.