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The inverse of \(f(x) = \frac{2x-1}{x+5}\) may be written in the form \(f^{-1}(x)=\frac{ax+b}{cx+d}\), where \(a\)\(b\)\(c\), and \(d\) are real numbers. Find \(a/c\).

 Apr 8, 2021

Best Answer 

 #1
avatar+33710 
+2

Swithch  x's and y's in the original equation and solve for y

 

x = (2y-1)/(y+5)

xy + 5x = 2y-1

 

5x + 1  = 2y-xy

5x+1 = y ( 2-x)

 

y =    (5x+1)/(-x+2)        <=======   you can finish from here I hope ! cheeky        

                                                                 (BTW   x cannot equal - 5 from original  and cannot equal 2 in the inverse) )

 Apr 8, 2021
edited by ElectricPavlov  Apr 8, 2021
edited by ElectricPavlov  Apr 8, 2021
 #1
avatar+33710 
+2
Best Answer

Swithch  x's and y's in the original equation and solve for y

 

x = (2y-1)/(y+5)

xy + 5x = 2y-1

 

5x + 1  = 2y-xy

5x+1 = y ( 2-x)

 

y =    (5x+1)/(-x+2)        <=======   you can finish from here I hope ! cheeky        

                                                                 (BTW   x cannot equal - 5 from original  and cannot equal 2 in the inverse) )

ElectricPavlov Apr 8, 2021
edited by ElectricPavlov  Apr 8, 2021
edited by ElectricPavlov  Apr 8, 2021
 #2
avatar
+1

I got -5, thanks! I was somewhat confused about the inverse.

 Apr 8, 2021

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