For every pair of continuous functions f, g: [0, 1] → R such that max{f(x): x ∈ [0, 1]} = max {g(x): x = [0, 1]}, the correct statement(s) is (are)

(A) (f(c))^{2} + 3f (c) = (g(c))^{2} + 3g(c) for some c ∈ [0, 1]

(B) (f(c))^{2} + f(c)=(g(c))^{2} + 3g(c) for some c ∈ [0, 1]

(C) (f(c))^{2} + 3f (c) = (g(c))^{2} + g(c) for some c ∈ [0, 1]

(D) (f(c))^{2} = (g(c))^{2} for some c ∈ [0, 1]