Inverses By: Jeffrey Bivin Lake Zurich High School Last Updated: November 17, 2005.
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Transcript of Inverses By: Jeffrey Bivin Lake Zurich High School Last Updated: November 17, 2005.
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Definition
Inverse Relation A relation obtained by switching the coordinates of each ordered pair.
Jeff Bivin -- LZHS
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INVERSE RELATIONS
Jeff Bivin -- LZHS
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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) }
Jeff Bivin -- LZHS
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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)}
Jeff Bivin -- LZHS
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f(x)= x2
Jeff Bivin -- LZHS
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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
Jeff Bivin -- LZHS
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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
Jeff Bivin -- LZHS
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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
Jeff Bivin -- LZHS
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Are these functions inverses?
35)( xxf53)(
xxg
xxxxfxgf
333535
53))((
xxxxgxfg
55
53)35()35())((
Jeff Bivin -- LZHS
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Are these functions inverses?
2)( xxf xxg )(
xxxfxgf 2
))((
)()())(( 22 xabsxxgxfg
Jeff Bivin -- LZHS