If f(x) = 2(x – 3)(^2) + 3(x – 3) + 4 and g(y) = (sqrt{5 + y}), find g [f(3)] and f[g(4)].

A.
3 and 4 
B.
3 and 4 
C.
3 and 4 
D.
3 and 4 
E.
0 and 5
Correct Answer: Option A
Explanation
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.