Restricting the Domain In Exercises 71–78, restrict the domain of the function f so that the function is one-to-one and has an inverse function. Then find the inverse function
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Precalculus (MindTap Course List)
- Exercises 31–38: Determine if f is a linear or nonlinear function. If f is a linear function, determine if f is a constant function. Support your answer by graphing f. -2 35. f (x) = |x + 1|arrow_forwardWhich of the functions graphed in Exercises 1–6 are one-to-one, and which are not?arrow_forwardExercises 65–74: Use the graph of f to determine intervals where f is increasing and where f is decreasing.arrow_forward
- Even and Odd FunctionsIn Exercises 47–58, say whether the function is even, odd, or neither. Give reasons for your answer.arrow_forwardIn Exercises 41–44, sketch a possible graph for a function f that hasthe stated properties.arrow_forward5. DISCUSS: Solving an Equation for an Unknown FunctionIn Exercises 69–72 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 Exercise 104), we can use algebra to solve such equations. Forinstance, to solve f g h for the unknown function f, weperform the following steps:arrow_forward
- Evaluating a Function In Exercises 5–12,evaluate the function at the given value(s) of theindependent variable. Simplify the results.f (x) = 3x − 2 (c) f (b)arrow_forwardIn Exercises 7–10, determine from its graph if the function is one-to-one.arrow_forwardIn Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see. 63. a. y = tan-1 (tan x) b. y = tan (tan-1 x) 64. a. y = sin-1 (sin x) b. y = sin (sin-1 x) 65. a. y = cos-1 (cos x) b. y = cos (cos-1 x)arrow_forward
- Find the natural domain and graph the functions in Exercises 15–20.arrow_forwardFor each graph in Exercises 61–72, find a function whosegraph looks like the one shown. When you are finished, usea graphing utility to check that your function f has the properties and features of the given graph.arrow_forwardInventing Graphs and FunctionsIn Exercises 75–78, sketch the graph of a function y = ƒ(x) that satisfies the given conditions. No formulas are required—just label the coordinate axes and sketch an appropriate graph. (The answers are not unique, so your graphs may not be exactly like those in the answer section.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage