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Math Help - Find Inverse Function

  1. #1
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    Find Inverse Function

    Given f(x) = (1/x + 2) + 3, find the inverse function.

    MY WORK:

    Let y = f(x).

    y = (1/x + 2) + 3

    Switch x and y.

    x = (1/y + 2) + 3

    Multiply both sides by (y+2).

    I ended up with

    xy + 2x = 3y + 7

    I then subtracted 3y and 2x from both sides.

    xy - 3y = -2x + 7

    I factored out a y from the left side.

    y(x - 3) = -2x + 7

    I finally divided both sides by (x - 3).

    y = (-2x + 7)/(x - 3)

    Then y becomes f^(-1) x

    f^(-1) x = (-2x + 7)/(x - 3)

    Is the right?

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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by magentarita View Post
    Given f(x) = (1/x + 2) + 3, find the inverse function.

    MY WORK:

    Let y = f(x).

    y = (1/x + 2) + 3

    Switch x and y.

    x = (1/y + 2) + 3

    Multiply both sides by (y+2).

    I ended up with

    xy + 2x = 3y + 7

    I then subtracted 3y and 2x from both sides.

    xy - 3y = -2x + 7

    I factored out a y from the left side.

    y(x - 3) = -2x + 7

    I finally divided both sides by (x - 3).

    y = (-2x + 7)/(x - 3)

    Then y becomes f^(-1) x

    f^(-1) x = (-2x + 7)/(x - 3)

    Is the right?

    it is correct
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  3. #3
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    Good...

    Quote Originally Posted by Amer View Post
    it is correct
    I placed this in another forum and was told my answer is wrong but I doubted them big time.
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  4. #4
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by magentarita View Post
    I placed this in another forum and was told my answer is wrong but I doubted them big time.
    but x\ne 3
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  5. #5
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    Yes...

    Quote Originally Posted by Amer View Post
    but x\ne 3
    Yes, x cannot = 3 because it creates division by zero.
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  6. #6
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    Given f(x) = (1/x + 2) + 3, find the inverse function.
    If you're not going to type in LaTex, please watch your parentheses next time! I interpreted the problem to be
    f(x) = \left(\frac{1}{x} + 2\right) + 3
    and was in the midst of writing a lengthy post correcting your work before I realized that you meant
    f(x) = \frac{1}{x + 2} + 3.
    Without LaTex, you should have written it as f(x) = 1/(x + 2) + 3.

    Argh...


    01
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  7. #7
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    ok...

    Quote Originally Posted by yeongil View Post
    If you're not going to type in LaTex, please watch your parentheses next time! I interpreted the problem to be
    f(x) = \left(\frac{1}{x} + 2\right) + 3
    and was in the midst of writing a lengthy post correcting your work before I realized that you meant
    f(x) = \frac{1}{x + 2} + 3.
    Without LaTex, you should have written it as f(x) = 1/(x + 2) + 3.

    Argh...


    01
    Thank you so much. I now see what went wrong.
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