+0  
 
0
102
1
avatar+247 

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 \(a/c\).

mathtoo  Mar 1, 2018

Best Answer 

 #1
avatar+12565 
+2

y = 2x-1/x+5         First, solve for 'x'    

  yx+5y -2x = -1

yx - 2x= -5y -1

x(y-2)  = -5y-1

x = (-5y-1)/(y-2)    then switch the x's and y's to have the inverse f^-1 (x)

y = (-5x-1)/(x-2)             a = -5 c= 1      a/c -5/1 = -5

ElectricPavlov  Mar 1, 2018
edited by ElectricPavlov  Mar 1, 2018
 #1
avatar+12565 
+2
Best Answer

y = 2x-1/x+5         First, solve for 'x'    

  yx+5y -2x = -1

yx - 2x= -5y -1

x(y-2)  = -5y-1

x = (-5y-1)/(y-2)    then switch the x's and y's to have the inverse f^-1 (x)

y = (-5x-1)/(x-2)             a = -5 c= 1      a/c -5/1 = -5

ElectricPavlov  Mar 1, 2018
edited by ElectricPavlov  Mar 1, 2018

15 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.