1. because 2 - x < 0 for x > 2

2. f(x) =

x+k^2, x<2

kx^2 + 14, x=>2

you want lim f(x) as x approaches 2- and 2+ to be the same:

2+k^2 = 4k + 14

k^2 -4k -12 = 0

(k-6)(k+2) = 0 k = 6 or -2

Where did the c come from ?x + k^2 = ck^2 + 14

x + k^2 - ck^2 - 14 = 0.