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posted by  browngirl on 11/4/2009 12:45:11 PM  |  status: Closed  |  Earned Karma: 0

inverse of a function

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Calculus Calculus (5th) by Stewart 3.2 N/A 11/4/2009 at 10:00:00 AM
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Good morning:
How do you find a formula for the inverse of the function.
f(x) = 8x-1/2x+7
Would you factor this before you do anything?
Thanks

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posted by velixy on 11/4/2009 1:06:06 PM  |  status: Live
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How do you find a formula for the inverse of the function.
f(x) = 8x-1/2x+7
 y=   f(x) =( 8x-1) / (2x+7)
y.(2x+7)  =  8x-1
 2xy +7y  = 8x  -1
2xy -8x  =  -1 -7y
 x ( 2y-8)  = -( 1+7y)
 x=  -( 1+7y)  /   ( 2y-8)
 f -1( x)= = -( 1+7x)  /   ( 2x-8)
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posted by anonymousxyz on 11/4/2009 1:11:00 PM  |  status: Live
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\begin{align*} & y = f( x ) = \frac{8x - 1}{2x + 7} \\\\& \text{Switch \textit{x} and \textit{y}, then solve for \textit{y}:}\\\\& \end{align*}


\begin{align*} & x = \frac{8y - 1}{2y + 7} &\Rightarrow\\\\& x( 2y + 7 ) = 8y -1 &\Rightarrow\\\\& 2xy + 7x - 8y + 1 = 0 &\Rightarrow\\\\& ( 2x - 8 )y = -(7x + 1) &\Rightarrow\\\\& y = -\frac{7x + 1}{ 2x - 8} &\Rightarrow\\\\& f^{-1}(x) = -\frac{7x + 1}{ 2x - 8} \end{align*}
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