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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 $$a/c$$.

mathtoo  Mar 1, 2018

#1
+12117
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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
Sort:

#1
+12117
+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

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