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korosh23

  • one year ago

Pre-calculus 12 question!

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  1. anonymous
    • one year ago
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    Whats the question

  2. korosh23
    • one year ago
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    One second

  3. korosh23
    • one year ago
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    1 Attachment
  4. korosh23
    • one year ago
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    It is about relation and inverse of relation

  5. korosh23
    • one year ago
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    What I am wondering is how the two lines in the graph are inverses of each other?

  6. anonymous
    • one year ago
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    Do u understand the inverse function?

  7. korosh23
    • one year ago
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    yes

  8. ganeshie8
    • one year ago
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    If \((a,b)\) is a point on \(f(x)\), then \((b,a)\) will be a point on its inverse.

  9. korosh23
    • one year ago
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    exactly

  10. ganeshie8
    • one year ago
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    Next, recall the transformation rule for reflection over line \(y=x\) : \[(x,y)\longrightarrow (y,x)\]

  11. anonymous
    • one year ago
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    i dont understand. if you understand the inverse function, why wouldn't the graph make sense?

  12. ganeshie8
    • one year ago
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    so, if two graphs are "symmetric" about the straight line \(y=x\), then they must be inverses of each other

  13. korosh23
    • one year ago
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    I don't understand the shape of the graph, how can you tell if it is inverse?

  14. korosh23
    • one year ago
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    oh I get it know @ganeshie8

  15. ganeshie8
    • one year ago
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    lets do couple of quick examples maybe

  16. korosh23
    • one year ago
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    sure

  17. ganeshie8
    • one year ago
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    lets find inverse of below graph : |dw:1439961068302:dw|

  18. ganeshie8
    • one year ago
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    Clearly, there is no easy way to find the inverse algebraically, you're forced to use geometry here

  19. korosh23
    • one year ago
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    right

  20. korosh23
    • one year ago
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    yes

  21. ganeshie8
    • one year ago
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    can you guess how the graph of inverse should look like ?

  22. korosh23
    • one year ago
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    |dw:1439954006748:dw|

  23. ganeshie8
    • one year ago
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    That's a very good "wrong" guess, remember, we want to reflect it over line \(y=x\), not over x axis

  24. ganeshie8
    • one year ago
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    let me just give you the answer, maybe you can try next example ok

  25. korosh23
    • one year ago
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    Actually I know it, can I get one more try?

  26. korosh23
    • one year ago
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    |dw:1439954141104:dw|

  27. ganeshie8
    • one year ago
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    Excellent! |dw:1439961311805:dw|