Match the functions in Column I with the properties Column II

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Match the functions in Column I with the properties Column II. Limit of gof doesn’t exist at x=−1\text{Limit of } gof \text{ doesn't exist at } x = -1
Column IColumn II
(A) g:R→Qg: R \to Q (Rational number); ff and gg are continuous functions such that 3f(x)+g(x)=3\sqrt{3} f(x) + g(x) = 3 , then (1−f(x))3+(g(x)−3)3(1 - f(x))^3 + (g(x) - 3)^3 is(p) 1
(B) If f(x)f(x) , g(x)g(x) and h(x)h(x) are continuous and positive functions such that f(x)+g(x)+h(x)=f(x)g(x)+g(x)h(x)+h(x)f(x)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)f(x) + g(x) - 2h(x) is(q) 0
(C) y=f(x)y = f(x) satisfies the equation y2−2y2(x+1)+4xy+(x2−1)(y−2)=0y^2 - 2y^2(x+1) + 4xy + (x^2-1)(y-2) = 0 , then y′(1)y'(1) would be equal to(r) 2
(D) If y=f(x)y = f(x) satisfies (xy′(x))98+(xy(x))98+⋯+(xy(x))+1=0(xy'(x))^{98} + (xy(x))^{98} + \dots + (xy(x)) + 1 = 0 , then (1+f′(1))(1 + f'(1)) is(s) 3
(t) -1

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