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Let f : [0, 1] → R be such that f(x y) = f(x).f(y), for all x, y ∈ [0, 1], and f(0) ≠ 0. If y = y(x)

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Let f : [0, 1] → R be such that f(x y) = f(x).f(y), for all x, y ∈ [0, 1], and f(0) ≠ 0. If y = y(x) satisfies the differential equation, dy/dx = f(x) with y(0) = 1, then y(1/4) + y(3/4) is equal to:

(1) 3

(2) 5

(3) 2

(4) 4

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The correct option (1) 3   

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