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 < 2, or k = 2 or k >2


Now, Case I: k < 2


Then, f(k) = 2k + 3


= 2k + 3= f(k)


Thus,


Hence, f is continuous at all real number less than 2.


Case II: k = 2


= 2×2 + 3 = 7


= 2×2 - 3 = 1



Hence, f is not continuous at x = 2.


Case III: k > 2


Then, f(k) = 2k - 3


= 2k – 3 = f(k)


Thus,


Hence, f is continuous at all real number greater than 2.


Therefore, x = 2 is the only point of discontinuity of f.


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