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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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.
Source: Myschool Past Questions Archive (Record #32424)