Question

f(x)=
−x+b, if x<−2
3, if x<−2
(-15/x-b) −2, x<−2 (and x≠b). For what value(s) of b is f(x) continuous?

Answer 1

To be continuous at x = -2, the left and right values must approach f(-2), so you need
-2+b = 3 = -15/(-2-b)
so check to be sure that both equalities hold for some value of b