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Unformatted text preview: ich takes 4 back to both x = 2 and x = −2. (By deﬁnition, a function matches
2 In other words, invertible functions have exactly one inverse.
It is an excellent exercise to explain each step in this string of equalities.
In the interests of full disclosure, the authors would like to admit that much of the discussion in the previous
paragraphs could have easily been avoided had we appealed to the description of a function as a set of ordered pairs.
We make no apology for our discussion from a function composition standpoint, however, since it exposes the reader
to more abstract ways of thinking of functions and inverses. We will revisit this concept again in Chapter 8.
3 296 Further Topics in Functions a real number with exactly one other real number.) From a graphical standpoint, we know that
if y = f −1 (x) exists, its graph can be obtained by reﬂecting y = x2 about the line y = x, in
accordance with Theorem 5.3. Doing so produces
(4, 2) 6
5 2 4 (−2, 4) 1 (2, 4)
3 1 2
1 −2 −1 2 3 4 5 6 7 x −1
1 y = f ( x) = x 2 2 x r...
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