Stitz-Zeager_College_Algebra_e-book

Express the total cost c of connecting the junction

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Unformatted text preview: ction by switching the inputs and outputs. Example 5.2.2. Find the inverse of the following one-to-one functions. Check your answers analytically using function composition and graphically. 1. f (x) = 1 − 2x 5 2. g (x) = 2x 1−x Solution. 1. As we mentioned earlier, it is possible to think our way through the inverse of f by recording the steps we apply to x and the order in which we apply them and then reversing those steps in the reverse order. We encourage the reader to do this. We, on the other hand, will practice the algorithm. We write y = f (x) and proceed to switch x and y 300 Further Topics in Functions y = f (x) 1 − 2x y= 5 1 − 2y x= 5 5x = 1 − 2y 5x − 1 = −2y 5x − 1 =y −2 y = −5x + 2 switch x and y 1 2 1 We have f −1 (x) = − 5 x+ 2 . To check this answer analytically, we first check that f −1 ◦ f (x) = 2 x for all x in the domain of f , which is all real numbers. f −1 ◦ f (x) = f −1 (f (x)) = − 5 f (x) + 2 1 2 1 − 2x + 5 = − 1 (1 − 2x) + 1 2 2 = −5 2 1...
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