Hello, North,
I'm a bit confused about the organization of the question, but will assume g(x) is a function with three distinct domains, as defined by the inequalities to the right of the functions.
g(x) is:
2x+1, for the range x<-2
x2-2, for the range -2≤x≤3
√x-10 for the range x>3
g(1) would point to the middle function as valid for this value of x, since -2≤x≤3
g(x) = x2-2
g(1) = 12 -2
g(1) = - 1
Bob