Find simplified form for f [g(x)]

Question

For  and  , find the simplified form for f [g(x)] and state the domain. 

Answer 1

f(x)=(1-x)/(1+x)

g(x)=x/(1+x)

f(g(x))=(1-[x/(1+x)])/(1+[x/1+x])

f(g(x))=((1+x-x)/(1+x)/((1+x+x)/(1+x))

f(g(x))=(1/(1+x))*(1+x)/(1+2x)

f(g(x()=1/(1+2x)

the domain is all real numbers except any number that makes the denominator equal to 0

so, 1+2x=0, 2x=-1, x=-1/2

the domain is all real numbers except -1/2