If `f(x)=-1+|x-2|,0lexle4`
`g(x)=2-|x|,-1lexle3`
Then find `fog(x)` and `gof(x)`. Also draw their rough sketch.

Explanation

To solve the problem, we need to find the compositions \( f(g(x)) \) and \( g(f(x)) \) for the given functions \( f(x) \) and \( g(x) \). Let's break this down step by step.

### Step 1: Define the Functions
The functions are given as:
- \( f(x) = -1 + |x - 2| \) for \( 0 \leq x \leq 4 \)
- \( g(x) = 2 - |x| \) for \( -1 \leq x \leq 3 \)

### Step 2: Find \( f(g(x)) \)
...