If f: R rarr R is a function such that f...

If f: R `rarr` R is a function such that f(x +y) =f(x) +f(y) `forall` x,y `in` R then f is continuous on R if it is continuous at a single point in R.

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The correct Answer is:

` rArr f(x) ` is continuous at any ` x in R `.
Hence f(x) is continuous on R .

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