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Math Help - Combination of Functions

  1. #1
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    Combination of Functions

    Find the inverse of each function.

    g)

    y = \frac {x + 5}{x -5}

    Where did I go wrong?

    x = \frac {y + 5}{y - 5}

    x(y - 5) = y + 5

    x(y - 5) -5 = y

    xy - 5x - 5 = y

    -5x - 5 = y - xy

    -5x - 5 = y(1 - x)

    \frac {-5x - 5}{1 - x} = y

    \frac {-5(x + 1)}{1 - x} = y

    Even if I move it to the right side. . .I get a different answer. . .

    y = \frac {5(x - 1)}{x - 1}

    Correct answer is. . .

    \frac {5(x + 1)}{x - 1}


    h)

    y = \frac {1}{x^2}

    Is my answer correct?

    x(y^2) = 1

    y^2 = \frac {1}{x}

    y = \sqrt{\frac {1}{x}}
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Macleef View Post
    Find the inverse of each function.

    g)

    y = \frac {x + 5}{x -5}

    Where did I go wrong?

    x = \frac {y + 5}{y - 5}

    x(y - 5) = y + 5

    x(y - 5) -5 = y

    xy - 5x - 5 = y

    -5x - 5 = y - xy

    -5x - 5 = y(1 - x)

    \frac {-5x - 5}{1 - x} = y

    \frac {-5(x + 1)}{1 - x} = y

    Even if I move it to the right side. . .I get a different answer. . .

    y = \frac {5(x - 1)}{x - 1}

    Correct answer is. . .

    \frac {5(x + 1)}{x - 1}
    You have:

    \frac {-5(x + 1)}{1 - x} = y

    or:

    y=\frac {-5(x + 1)}{1 - x}=\frac{5(x+1)}{(x-1)}

    (that is multiply top and bottom of the middle term side by -1 to get the right most term, which is the desired answer)
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Macleef View Post
    h)

    y = \frac {1}{x^2}

    Is my answer correct?

    x(y^2) = 1

    y^2 = \frac {1}{x}

    y = \sqrt{\frac {1}{x}}
    Subject to the restriction that x > 0 yes except that you have reversed the meaning of x and y.


    y(x^2) = 1

    x^2 = \frac {1}{y}

    x = \sqrt{\frac {1}{y}}

    when y > 0


    RonL
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