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Let f: (-oo,oo) to (-oo,oo) be such that f(.) is continuous at 0 and let f((x+y)/2) = (f(x)+f(y))/2 for x , y in (-oo,oo) Statement-1: f(.) is continuous at every point on (-oo,oo) Statement-2: f(x+h)+f(0)=2 f(x)+f(2h) for x , h in (-oo, oo). |
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