8.Prove that the identity function on real numbers given by f(x) = x is continuous at every real number.
Here f(x) = x Function f is defined for all real numbers Let c be any real number.
∴ f is continuous at x = c But c is any real number. ∴ f is continuous at every real number.
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9.Show that the function defined by g(x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x
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10.Find all the points of discontinuity of the greatest integer function defined by f(x) = [x], where [x] denotes the greatest integer less than or equal to x.