+0

The inverse of may be written in the form , where , , , and are real numbers. Find ​.

0
46
2

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

#1
+31577
+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 !

(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
+31577
+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 !

(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
+1

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

Apr 8, 2021