Inverses

By: Jeffrey BivinLake Zurich High School

jeff.bivin@lz95.org

Last Updated: November 17, 2005

Definition

Inverse Relation A relation obtained by switching the coordinates of each ordered pair.

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INVERSE RELATIONS

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Relation { (1, 4), (4, 6), (-3, 2), (-4, -2), (-1,5), (0, 1) }

Inverse { (4, 1), (6, 4), (2, -3), (-2, -4), (5, -1), (1, 0) }

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Inverse {(-6,-4), (4,1), (6, 2), (0,-1), (3,-4), (-2,4)}

Relation {(-4,-6), (1,4), (2, 6), (-1,0), (-4,3), (4,-2)}

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f(x)= x2

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f(x)= x2

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G(x)

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G(x)

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G(x)

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G(x)

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f(x)= x3

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Find the inverse23)( xxf23 yx

yx 32

yx

32

321

xxf

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Find the inverse2)( xxf 2yx

yx

xxfinv

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Find the inverse5)( 2 xxf52 yx

25 yx

5 xxfinv

yx 5

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Inverse functions

Two functions, f(x) and g(x), areinverses of each other if and only if:

f(g(x)) = xand

g(f(x)) = x

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Are these functions inverses?

35)( xxf53)(

xxg

xxxxfxgf

333535

53))((

xxxxgxfg

55

53)35()35())((

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Are these functions inverses?

2)( xxf xxg )(

xxxfxgf 2

))((

)()())(( 22 xabsxxgxfg

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