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.