Answer: (-∞, -1] and (0, 2)
Explanation:
Can't compare f(x) = x+1 when x<=0 with g(x)=x+1 when x>-1 since the functions are equal between -1<x<=0.
Compare f(x) = 3 when x>0 with g(x)=x+1 when x>-1
g(x) can't be greater than or equal to f(x):
g(x)<f(x)
x+1<3
x+1-1<3-1
x<2 and x>0 ==> 0<x<2
0<x<2 ==> (0, 2) ==> x is between 0 and 2 not including 0 and 2.
Compare f(x) = x+1 when x<=0 with g(x)=2x when x<=-1. Both equations have common x-values at x<=-1.
g(x)<f(x)
2x<x+1
2x-x<x-x+1
x<1 and x<=-1 ==> x<=-1
x<=-1 ==> (-∞, -1] ==> x is between -∞ and -1 not including -∞ but including -1.
(-∞, -1] and (0, 2)