Rewrite as piecewise + domain + range?

[Wa1337]

Homework Statement

1. Rewrite as piecewise: g(x) = 2x - |3x-2|

2. Give domain and equation represented by f(g(x)) when g(x) = √(x+1) and f(x) = 3/x

3. Give range of P(x) = {2x-1, x >/= 1
{x^2 + 1, -1 </= x < 1
{√|x|, x<-1

thanks in advance

Homework Equations

The Attempt at a Solution

for #1 I got: G(x) = 2x -|3x-2| = {-x + 2, x >/= 2/3
{5x - 2, x < 2/3

 

[grief]

What are you thoughts on numbers 2 and 3?

For number 2, note that the domain of f(x) is the set of all points but 0, since you're not allowed to divide by 0. The domain of g(x) is all x>=-1 (or else you'd be taking the square root of a negative number, which is not allowed, either). How do you combine this information to determine the domain of f(g(x))?