The graphs of f and f -1

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The graphs of f and f -1

• How are they related?

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Some Preliminary Thoughts Suppose we have some
points in the plane . . .
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What happens if we switch their x and y
coordinates?
(1,5)
(3,3)
(-4,2)
(2,-2)
(-1,-1)
4
(1,5)
(3,3)
(-4,2)
(-2,2)
(5,1)
(2,-2)
(-1,-1)
(2,-4)
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(1,5)
(3,3)
(-4,2)
(-2,2)
(5,1)
(2,-2)
The line y x serves as amirror!
(-1,-1)
(2,-4)
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(1,5)
(3,3)
(-4,2)
(-2,2)
(5,1)
(-1,-1)
(2,-2)
That is, each point is reflected across the line
y x.
(2,-4)
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(4,6)
Suppose we have a one-to-one function f. To get
f -1 from f, we switch every x and y coordinate.
f -1
(2,3)
(6,4)
f
(3,2)
(-1,-1)
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Lets try another example.
f -1
(1,5)
f
(5,1)
(-0.5,-3)
(-0.5,-3)
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Lets try another example.
f -1
f
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One last example. . .
f -1
f
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One last example. . .
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One last example. . .
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One last example. . .