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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.
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
the job for all x in the domain of f , we take the generic...
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