How do you find the inverse of #f(x)=ln(x-1) - ln(2x +1)#?

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Answer 1 · 2016-07-20T07:59:38

#f^-1(x)=(e^x+1)/(1-2e^x)#

Let
#y=f(x)=ln(x-1)-ln(2x+1)#

#=>y=ln((x-1)/(2x+1))#

#=>(x-1)/(2x+1)=e^y#

#=>2xe^y+e^y=x-1#

#=>x(1-2e^y)=e^y+1#

#:.x=(e^y+1)/(1-2e^y)#

So the inverse function of f(x) will be

#f^-1(x)=(e^x+1)/(1-2e^x)#