If `f(x) = -1 +|x-1|, -1 le x le 3 " and " g(x)=2-|x+1|, -2 le x le 2,` then find `fog(x) " and " gof(x).`

Explanation

To solve the problem, we need to find the compositions \( f(g(x)) \) and \( g(f(x)) \) given the functions:

1. \( f(x) = -1 + |x - 1| \) for \( -1 \leq x \leq 3 \)
2. \( g(x) = 2 - |x + 1| \) for \( -2 \leq x \leq 2 \)

### Step 1: Find \( f(g(x)) \)

First, we need to determine the expression for \( g(x) \):
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