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the inverse of function f(x) = (2x-2)/(x-5) is written in the form of $f^{-1}(x)=\dfrac{ax+b}{cx+d}$, where a, b, c, and d are all real numbers. Find a/c.

 Jul 11, 2022
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y = (2x - 2) / (x - 5)              get x by itself

 

y (x - 5) =  (2x -2)

 

xy - 5y  = 2x  - 2

 

xy  - 2x  =  5y - 2

 

x ( y -2)  = (5y -2)

 

x =  (5y -2)  / ( y -2)            exchange x, y

 

y = (5x -2) / ( x  - 2)  =   f-1(x)  

 

a = 5     c   =1

 

a / c  =  5  / 1    =  5

 

 

cool cool cool

 Jul 11, 2022

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