how do you solve this

Question

Simplify the composite function f of g and state its domain

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

g(x)=2/x

Answer 1

f(g(x)) = f(2/x) = (2/x)/(1-(2/x)^2 = 2/x(1-4/x^2) = 2/(x -4/x)

domain is all real numbers except where the denominator =0

except where x-4/x =0, x^2-4=0, x= +/-2

domain is (-infinity,-2) U (-2,2) U (2, infinity)

domain is all reall numbers except x=-2 and x=2