# Rewrite as piecewise + domain + range?

1. Sep 13, 2011

### Wa1337

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. The attempt at a solution
for #1 I got: G(x) = 2x -|3x-2| = {-x + 2, x >/= 2/3
{5x - 2, x < 2/3

Last edited: Sep 13, 2011
2. Sep 14, 2011

### 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))?