Help on calculus please!

Question

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

Answer 1

f(2) means you plug the number 2 into f(x) wherever there is an "x" so f(2) = (1 - 2)/(1 + 2) = -1/3

The same thing holds true for f(g(x)), you plug in g(x) into the function f(x) wherever there is an "x" and g(x) is x/(1 - x) so you plug that into f(x) wherever there is an "x" to get:

To simplify, get a common denominator ("1 - x") to combine the two parts of the numerator and then do the same for the denominator. When you finish, you'll get f(g(x)) = 1 - 2x

The domain can be any number except 1 because that value of x would give a 0 in the denominator of the expression above. We write that as the domain is (-∞, 1) ∪ (1, ∞)