Unformatted text preview: s natural to wonder what f −1 (x) and g −1 (x) would be. For f (x) = 1−2x , we can
think our way through the inverse since there is only one occurrence of x. We can track step-by-step
what is done to x and reverse those steps as we did at the beginning of the chapter. The function
g (x) = 12xx is a bit trickier since x occurs in two places. When one evaluates g (x) for a speciﬁc
value of x, which is ﬁrst, the 2x or the 1 − x? We can imagine functions more complicated than
these so we need to develop a general methodology to attack this problem. Theorem 5.2 tells us
equation y = f −1 (x) is equivalent to f (y ) = x and this is the basis of our algorithm.
Steps for ﬁnding the Inverse of a One-to-one Function
1. Write y = f (x)
2. Interchange x and y
3. Solve x = f (y ) for y to obtain y = f −1 (x)
Note that we could have simply written ‘Solve x = f (y ) for y ’ and be done with it. The act of
interchanging the x and y is there to remind us that we are ﬁnding the inverse fun...
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