home > q&a board > algebra thru pre-calculus > topic: please help find the inverse function!

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posted by  mike88 on 10/6/2008 10:06:54 PM  |  status: Live  

please help find the inverse function!

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\displaystyle f(x) = \frac{x}{x-3}. Find f.
f^{-1}(x) = .
Now for fun, verify that (f\circ f^{-1})(x)=(f^{-1}\circ f)(x)=x
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posted by Leith on 10/6/2008 10:19:59 PM  |  status: Live
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Response Details:
To find inverse function you switch x's and y's and then solve for y

so x= y/(y-3)

x(y-3) = y
xy-3x= y
xy-y = 3x
y(x-1) = 3x
y= 3x/(x-1)
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posted by Cacing on 10/6/2008 10:25:37 PM  |  status: Live
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Response Details:
Question Details:
\displaystyle f(x) = \frac{x}{x-3}. Find f.

       y = y (x - 3 ) = x yx - 3y = x yx - x = 3y x(y - 1) = 3y x =
    f =
  
f^{-1}(x) = .
Now for fun, verify that (f\circ f^{-1})(x)=(f^{-1}\circ f)(x)=x
                               =
                                =
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