Answer:
f(g(x))=1-2x
domain is set of all x values except 1
Step-by-step explanation:
[tex]f(x)=\frac{1-x}{1+x} \\g(x)=\frac{x}{1-x}[/tex]
we use composition of function f(g(x))
Plug in g(x) inside f(x)
[tex]f(g(x))= f(\frac{x}{1-x})\\f(g(x))=\frac{1-\frac{x}{1-x}}{1+\frac{x}{1-x}} \\\\f(g(x))=\frac{\frac{1-x-x}{1-x}}{\frac{1-x+x}{1-x}} \\\\\\f(g(x))=\frac{\frac{1-2x}{1-x}}{\frac{1}{1-x}} \\\\\\\\f(g(x))=1-2x[/tex]
Domain is the set of x values for which the function is defined
for domain set 1-x=0
x=1
domain is set of all x values except 1
