Question

determine the inverse of g(x) = x/1-x and the domain and range of g(x) and inverse of g(x)

Answer 1

domain all real number except x=1
range real numbers
for inverse g(x)=x/(1-x)
g(x)*(1-x)=x
g(x)-x*g(x)=x
g(x)=x+x*g(x)
g(x)=x*(1+g(x))
g(x)/(1+g(x))=x
replace x by g^-1(x)
x/(1+x)=g(x) inverse