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
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.
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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