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Math Help - Inverse functions

  1. #1
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    Inverse functions

    what is the inverse function of 3y=2x+7. How will I do that? thanks
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    MHF Contributor chisigma's Avatar
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    Any linear function of the type  y= a\cdot x + b , a \ne 0 has its inverse of the form  x= \frac {1}{a}\cdot (y-b). In your case is a=\frac {2}{3} , b= \frac{7}{3}

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    \chi \sigma
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  3. #3
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    Quote Originally Posted by chisigma View Post
    Any linear function of the type  y= a\cdot x + b , a \ne 0 has its inverse of the form  x= \frac {1}{a}\cdot (y-b). In your case is a=\frac {2}{3} , b= \frac{7}{3}

    Kind regards

    \chi \sigma
    you mean that the inverse of y=f(x) is x=f(y)?? I will just make it in terms of x

    in my question

    3y=2x+7

    3y-7=2x

    f(x)=\frac{3y-7}{2}
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  4. #4
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by princess_21 View Post
    you mean that the inverse of y=f(x) is x=f(y)??...
    More exactly the inverse of y=f(x) is x=f^{-1} (y)

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    \chi \sigma
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  5. #5
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    [quote=chisigma;286895]More exactly the inverse of y=f(x) is x=f^{-1} (y)

    can you give an example? i cant understand. x=f^{-1} (y)
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  6. #6
    MHF Contributor chisigma's Avatar
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    Simple examples of couples of 'direct' and 'inverse' functions are...

    y=f(x)=x^{2} \rightarrow x=f^{-1} (y)= \sqrt {y}

    y= f(x)= \sin x \rightarrow x=f^{-1} (y)= \sin ^{-1} y

    y= f(x) = e^{x} \rightarrow x=f^{-1} (y)= \ln y

    In it important to take into account that the inverse function often it is not a single value function, just as in three examples I have given…

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    \chi \sigma
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