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Let f(x) = [x], where [·] is the greatest integer function and g(x) = sin x be two real valued functions over R.

Which of the following statements is correct ?

Mathematics 2016 NDA Mathematics 2016 NDA 2016

Options

Both f(x) and g(x) are continuous at x = 0.

f(x) is continuous at x = 0, but g(x) is not continuous at x = 0.

g(x) is continuous at x = 0, but f(x) is not continuous at x = 0.

Both f(x) and g(x) are discontinuous at x = 0.