Question

Find the inverse of f(x)=ln(x/x-2). Can someone please explain to me how I find the answer?

Answer 1

1. first to find the inverse of a function that function has to be bijective( so you have to prove that function is both injective and surjective)

1.first you prove it s injective then surjective -> bijective -> inversab

2 f-1:B-> A


.y=ln(x/x-2)
ln10^y=ln(x/x-2)
x/x-2=10^y
x=10^y*x-2*10^y
x-10^y*x=-2*10^y
x(1-10^y)= -2*10^y
x= -2*10^y/(1-10^y);

f-1(x)= -2*10^x/(1-10^x);