Find the simplified form for f [g(x)] and state the domain

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))---> Read it as " f of g of x. It means that we evaluate g(x) and use that value for the independent variable in g(x).

Note: g(x) appears to be missing a "(". I think it should be as written below:

So...write f(x) and then replace the x with the value of g(x), which is (x)/(1-x)

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

multiply top and bottom by 1-x:

(1 - x - x)/(1 - x + x)

1 - 2x