Q. 63.8( 61 Votes )
Find all points of discontinuity of f, where f is defined by
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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