Question

For f(x)=1-x/1+x and g(x)=x/1-x, find the simplified form for f[g(x)] and state the domain

Answer 1

f(g(x))=1-2x

domain is set of all x values except 1

Explanation:

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

we use composition of function f(g(x))

Plug in g(x) inside f(x)

`f(g(x))= f((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))=((1-2x)/(1-x))/((1)/(1-x)) \\\\\\\\f(g(x))=1-2x`

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