Unformatted text preview: Example
The graph of the function y = f (x) is given below. Use this graph to ﬁnd f −1 (x)
at x = 3 and x = 6. 6 5 4 3 2 1 1 2 3 4 5 Solution: The function f graphed above is invertible because it passes the horizontal line
test. The relationship between f (x) and f −1 (x) can be stated as follows:
The point (a, b) is on the curve y = f (x) if and
only if the point (b, a) is on curve y = f −1 (x).
We are ﬁrst asked to ﬁnd f −1 (x) when x = 3, i.e., to ﬁnd f −1 (3). But the point (3, f −1 (3)) is
on the curve y = f −1 (x) if and only if (f −1 (3), 3) is on the curve y = f (x). Looking at the
above graph we see that the point (1, 3) is on the curve y = f (x), so
f −1 (3) = 1.
Similarly, to ﬁnd f −1 (6) we note that the point (6, f −1 (6)) is on the curve y = f −1 (x) if and
only if the point (f −1 (6), 6) is on the curve y = f (x). Again looking at the above graph we
see that 6 = f (4), so the point (4, 6) is on the graph of y = f (x), and therefore
f −1 (6) = 4. ...
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.
 Fall '10
 KIHYUNHYUN
 Calculus

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