f(x) = 2(x - 3)\(^2\) + 3(x - 3) + 4

= (2 + 3) (x - 3) + 4

= 5(x - 3) + 4

= 5x - 15 + 4

= 5x - 11

f(3) = 5 x 3 - 11

= 4

g(f(3)) = g(4)

= \(\sqrt{5 + 4}\)

= \(\sqrt{9}\)

= 3

g(4) = 3

f(g(4)) = f(3)

= 4

g[f(3)] and f[g(4)] = 3 and 4 respectively.