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

1 Answer
Jul 20, 2016

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

Explanation:

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)