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Math Help - Find invarient point(s) Algebraically

  1. #1
    Raj
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    Find invarient point(s) Algebraically

    Given f(x) = 3x -6, algebraically determine y = f^-1(x) and the invarient point(s).

    y = 3x - 6
    x = 3y - 6
    x + 6 = 3y
    y = \frac{x}{3} + 2

    That is as far as I got. I know the answer is (3,3), but how do i show this.
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  2. #2
    Flow Master
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    Quote Originally Posted by Raj View Post
    Given f(x) = 3x -6, algebraically determine y = f^-1(x) and the invarient point(s).

    y = 3x - 6
    x = 3y - 6
    x + 6 = 3y
    y = \frac{x}{3} + 2

    That is as far as I got. I know the answer is (3,3), but how do i show this.
    Solve f(x) = f^{-1}(x), that is, 3x - 6 = \frac{x}{3} + 2.
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  3. #3
    Raj
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    Quote Originally Posted by mr fantastic View Post
    Solve f(x) = f^{-1}(x), that is, 3x - 6 = \frac{x}{3} + 2.
    Ok x = 3

    What about the y-value? Do I just sub that into the second or first equation?
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  4. #4
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    Quote Originally Posted by Raj View Post
    Ok x = 3

    What about the y-value? Do I just sub that into the second or first equation?
    Do you think it matters ..... ? Substitute into both. What do you find? What other line must this point lie on? Does this surprise you?
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