Mathematics

Problem

Match the functions in Column I with the properties Column II.

\text{Limit of } gof \text{ doesn't exist at } x = -1

Column I	Column II
(A) $g: R \to Q$ (Rational number); $f$ and $g$ are continuous functions such that $\sqrt{3} f(x) + g(x) = 3$ , then $(1 - f(x))^3 + (g(x) - 3)^3$ is	(p) 1
(B) If $f(x)$ , $g(x)$ and $h(x)$ are continuous and positive functions such that $f(x) + g(x) + h(x) = \sqrt{f(x)g(x)} + \sqrt{g(x)h(x)} + \sqrt{h(x)f(x)}$ , then $f(x) + g(x) - 2h(x)$ is	(q) 0
(C) $y = f(x)$ satisfies the equation $y^2 - 2y^2(x+1) + 4xy + (x^2-1)(y-2) = 0$ , then $y'(1)$ would be equal to	(r) 2
(D) If $y = f(x)$ satisfies $(xy'(x))^{98} + (xy(x))^{98} + \dots + (xy(x)) + 1 = 0$ , then $(1 + f'(1))$ is	(s) 3
	(t) -1