1. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org
Inverses
By: Jeffrey Bivin
Lake Zurich High School
Last Updated: November 17, 2005

2. Definition
Inverse Relation  A relation obtained by switching the coordinates of each ordered pair.
Jeff Bivin -- LZHS

3. INVERSE RELATIONS x y { (3, 8) } relation Domain Range 3 8 inverse
{ (8, 3) }
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4. y = x 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) }
y = x
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5. y = x Relation  {(-4,-6), (1,4), (2, 6), (-1,0), (-4,3), (4,-2)}
Inverse  {(-6,-4), (4,1), (6, 2), (0,-1), (3,-4), (-2,4)}
y = x
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6. f(x)= x2
y = x
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7. f(x)= x2
y = x
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8. G(x)
y = x
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9. G(x)
y = x
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10. G(x)
y = x
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11. G(x)
y = x
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12. f(x)= x3
y = x
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13. Find the inverse
Is this a function?
YES
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14. Find the inverse
Is this a function? NO
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15. Find the inverse
Is this a function? NO
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16. f(g(x)) = x and g(f(x)) = x
Inverse functions
Two functions, f(x) and g(x), are
inverses of each other if and only if:
f(g(x)) = x
and
g(f(x)) = x
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17. Are these functions inverses?
Therefore: Inverses
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18. Are these functions inverses?
Therefore: NOT Inverses
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19. One-to-One functions
A function is one-to-one if no two elements in the domain of the function correspond to the same element in the range.
Domain
Range 2 1
F(x)
One-to-One 5 -5 9 4
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20. f(x)= x2
y = x
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