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Sketch the graph of the function f(x)=square root X

  1. Mar 28, 2006 #1

    Aka

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    a) sketch the graph of the function f(x)=square root X
    b) on the same set of axes, graph y=f^-1(x), y=-f^-1(-x)

    so I did a chart, but i dont know if its right...I don't think its right :confused:

    f(x)=squareroot x

    X Y
    0 0
    1 1
    4 2
    9 3

    y=f^-1(x)

    X Y
    0 0
    1 -1
    4 -2
    9 -3

    y=-f^-1(-x)

    X Y
    0 0
    -1 1
    -4 2
    -9 3

    and i don't understand the question
    if the two graph of y=-f^-1(-x) is drawn from the graph of y=f(x) by a single reflection, what is the equation of the reflection line?

    Thanks
     
  2. jcsd
  3. Mar 29, 2006 #2

    Tide

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    Science Advisor
    Homework Helper

    The graph of the inverse function will be the reflection of the function about the line y = x which amounts to exchanging the values of x and y in your tables and adjusting accordingly for the negative of the inverse.
     
  4. Mar 29, 2006 #3

    HallsofIvy

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    Staff Emeritus
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    Yes, this is correct.

    No, this is y= -f(x), not y= f-1(x), the inverse function.
    To get the inverse function, just swap the x and y columns.
    What is the "opposite" of square root?

    [/quote]y=-f^-1(-x)

    X Y
    0 0
    -1 1
    -4 2
    -9 3 [/quote]
    see above.

    I don't understand "the two graph". Are you sure that you have copied the problem correctly? Draw the graphs as you were told two. Is there some line so that "flipping" the first graph over that line gives the second graph?
     
  5. Mar 29, 2006 #4

    Aka

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    ^ Thanks
    sorry, I did not coppy it corrently, it's not supposed to have the two in it :P

    so is it like this?

    y=f^-1(x)
    X Y
    0 0
    1 1
    2 4
    3 9

    y=f^-1(-x)
    X Y
    0 0
    -1 1
    -2 4
    -3 9
     
  6. Mar 29, 2006 #5
    Yes, that's better. But, I believe you forgot the negative in front of the f^-1 in the second equation. Shouldn't that be y = -f^-1(-x)?
     
  7. Mar 29, 2006 #6

    Aka

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    ^ yes, it should

    so the y values will be negative
     
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