Let f:[0,1]→R be such that f(xy)=f(x)⋅f(y), for all x,y∈[0,1], a – InterviewSolution

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1.	Let f:[0,1]→R be such that f(xy)=f(x)⋅f(y), for all x,y∈[0,1], and f(0)≠0. If y=y(x) satisfies the differential equation, dydx=f(x) with y(0)=1,then y(14)+y(34) is equal to :
Answer» Let $f : [0, 1] \to R$ be such that $f (x y) = f (x) \cdot f (y)$ , for all $x, y \in [0, 1]$ , and $f (0) \neq 0$ . If $y = y (x)$ satisfies the differential equation, $\frac{d y}{d x} = f (x)$ with $y (0) = 1, then y (\frac{1}{4}) + y (\frac{3}{4})$ is equal to :

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