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Thread: 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 $\displaystyle y= a\cdot x + b$ , $\displaystyle a \ne 0$ has its inverse of the form $\displaystyle x= \frac {1}{a}\cdot (y-b)$. In your case is $\displaystyle a=\frac {2}{3}$ , $\displaystyle b= \frac{7}{3}$

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

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
    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

    $\displaystyle 3y=2x+7$

    $\displaystyle 3y-7=2x$

    $\displaystyle f(x)=\frac{3y-7}{2}$
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    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 $\displaystyle y=f(x)$ is $\displaystyle x=f^{-1} (y)$

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

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

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

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

    $\displaystyle 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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    $\displaystyle \chi$ $\displaystyle \sigma$
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