Q. 13 4.1( 9 Votes )

Is the function defined by



a continuous function?

Answer :

The given function is

The function f is defined at all points of the real line.


Let k be the point on a real line.


Then, we have 3 cases i.e., k < 1, or k = 1 or k > 1


Now,


Case I: k < 1


Then, f(k) = k + 5


= k + 5 = f(k)


Thus,


Hence, f is continuous at all real number less than 1.


Case II: k = 1


Then, f(k) = f(1) = 1 + 5 = 6


= 1 + 5 = 6


= 1 - 5 = -4



Hence, f is not continuous at x = 1.


Case III: k > 1


Then, f(k) = k -5


= k - 5


Thus,


Hence, f is continuous at all real number greater than 1.


Therefore, x = 1 is the only point of discontinuity of f.


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