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Examine the following functions for continuity.
(a) 
(b) 
(c) 
(d) 
Asked by Vg.manikandan Last Modified
Answer (a) The given function is
It is evident that f is defined at every real number k and its value at k is k − 5.
It is also observed that, 
Hence, f is continuous at every real number and therefore, it is a continuous function.
(b) The given function is
For any real number k ≠ 5, we obtain
Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.
(c) The given function is
For any real number c ≠ −5, we obtain
Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.
(d) The given function is 
This function f is defined at all points of the real line.
Let c be a point on a real line. Then, c < 5 or c = 5 or c > 5
Case I: c < 5
Then, f (c) = 5 − c
Therefore, f is continuous at all real numbers less than 5.
Case II : c = 5
Then, 
Therefore, f is continuous at x = 5
Case III: c > 5
Therefore, f is continuous at all real numbers greater than 5.
Hence, f is continuous at every real number and therefore, it is a continuous function.
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