Stitz-Zeager_College_Algebra_e-book

Consider the expression x23 applying 32 23 the usual

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Unformatted text preview: fe, we will find that some processes (like putting on socks and shoes) are reversible while some (like cooking a steak) are not. We start by discussing a very basic function which is reversible, f (x) = 3x + 4. Thinking of f as a process, we start with an input x and apply two steps, as we saw in Section 1.5 1. multiply by 3 2. add 4 To reverse this process, we seek a function g which will undo each of these steps and take the output from f , 3x + 4, and return the input x. If we think of the real-world reversible two-step process of first putting on socks then putting on shoes, to reverse the process, we first take off the shoes, and then we take off the socks. In much the same way, the function g should undo the second step of f first. That is, the function g should 1. subtract 4 2. divide by 3 Following this procedure, we get g (x) = x−4 . Let’s check to see if the function g does the job. 3 If x = 5, then f (5) = 3(5) + 4 = 15 + 4 = 19. Taking the output 19 from f , we substitute it − into g to get g (19) = 193 4 = 15 = 5, which is our original input to f . To check that g does 3 the job for all x in the domain of f , we take the generic...
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