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Let f: (-oo,oo) to (-oo,oo) be such that...

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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