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Math Help - inverse of a function

  1. #1
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    inverse of a function

    Im trying to find the inverse of the function with working, see attached image
    Attached Thumbnails Attached Thumbnails inverse of a function-ica1-specimen-3.jpg  
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  2. #2
    Super Member Bacterius's Avatar
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    f(x) = \frac{2 - 3x}{4x + 5}

    Say f(x) = y

    y = \frac{2 - 3x}{4x + 5}

    Thus :

    y(4x + 5) = 2 - 3x

    Expand :

    4xy + 5y = 2 - 3x

    Rearrange terms :

    4xy + 3x = 2 - 5y

    Factorize x :

    x(4y + 3) = 2 - 5y

    Make x the subject by dividing :

    x = \frac{2 - 5y}{4y + 3}

    Thus the inverse function of f(x) is f(x)^{-1} = \frac{2 - 5x}{4x + 3}

    Does it make sense ?
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  3. #3
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    Cheers Ray that is spot on
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  4. #4
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    Smile

    put y=\frac{2-3x}{4x+5},flip x and y , x=\frac{2-3y}{4y+5} and solve for y.
    x=\frac{2-3y}{4y+5}\Leftrightarrow x\left ( 4y+5 \right )= 2-3y\Leftrightarrow 4xy+3y+5x= 2\Leftrightarrow y\left ( 4x+3 \right )= 2-5x\Leftrightarrow y=\frac{2-5x}{4x+3}
    and hence the inverse is f^{-1}(x)=\frac{2-5x}{4x+3}
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  5. #5
    Super Member Bacterius's Avatar
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    Quote Originally Posted by hunterage2000 View Post
    Cheers Ray that is spot on
    By the way, this trick can help you find answers easily so as to be able to solve this type of questions quicker : can you spot some kind of relation between the numbers in the function and the numbers in the inverse function ?

    EDIT : woah Raoh now this is "compressed" maths, now I realize how much of a waste of paper my writing style would be in an exam . I detailed carefully each step because Hunterage asked for it though .
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  6. #6
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    Quote Originally Posted by Bacterius View Post
    By the way, this trick can help you find answers easily so as to be able to solve this type of questions quicker : can you spot some kind of relation between the numbers in the function and the numbers in the inverse function ?

    EDIT : woah Raoh now this is "compressed" maths, now I realize how much of a waste of paper my writing style would be in an exam . I detailed carefully each step because Hunterage asked for it though .
    Yes but I founds yours easier to follow. Bear in mind that x=-\frac{5}{4} is not in the domain of f(x)
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