g(x) is a piecewise function in such a way that it changes how it's defined based on what x happens to be. There are three cases
Case A: g(x) = x-1 but only if [tex]-2 \le x < -1[/tex] (x is between -2 and -1; including -2 but excluding -1)
Case B: g(x) = 2x+3 but only when [tex]-1 \le x < 3[/tex] (x is between -1 and 3; including -1 but excluding 3)
Case C: g(x) = 6-x but only when [tex]x \ge 3[/tex]
The input is x = 3 since we want to find the value of g(3). So we look at the 3 cases above (A,B,C) and determine that we use case C. Why? Because x = 3 makes [tex]x \ge 3[/tex] true. Put another way, x = 3 is in the interval [3, infinty). So we'll use g(x) = 6-x to find that...
g(x) = 6-x
g(3) = 6-3
g(3) = 3
Answer: 3
