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Math Help - Compsite and Inverse Functions

  1. #1
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    Compsite and Inverse Functions

    I need help on what seems very simple

    f-1(x)=1/(x+6).. so at first I tried simple replace to get the inverse..

    y=1/x+6
    x=1/y+6
    then the inverse making the answer y+6 to no avail.

    can you help me understand where I went wrong?
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  2. #2
    Senior Member eumyang's Avatar
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    Not sure what you are asking. It looks like you're given f^{-1}(x) and you're trying to find f(x)? If so:
    f^{-1}(x)=\dfrac{1}{x+6}

    If we let f^{-1}(x) = y and swap the variables (which is what it looks like you did) we get:
    \begin{aligned}<br />
y &= \frac{1}{x+6} \\<br />
x &= \frac{1}{y+6} \\<br />
x(y + 6) &= 1 \\<br />
y + 6 &= \frac{1}{x} \\<br />
y &= \dfrac{1}{x} - 6<br />
\end{aligned}

    So f(x) = \dfrac{1}{x} - 6.
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