Question -
Answer -
(a) The given function is
It isevident that f is defined at every real number k andits value at k is k − 5.
It is also observedthat, 
Hence, f iscontinuous at every real number and therefore, it is a continuous function.
(b) The givenfunction is
Forany real number k ≠ 5, we obtain
Hence, f iscontinuous at every point in the domain of f and therefore, itis a continuous function.
(c) The givenfunction is
Forany real number c ≠ −5, we obtain
Hence, f iscontinuous at every point in the domain of f and therefore, itis a continuous function.
(d) The given function is 
Thisfunction f is defined at all points of the real line.
Let c bea point on a real line. Then, c < 5 or c =5 or c > 5
CaseI: c < 5
Then, f (c)= 5 − c
Therefore, f iscontinuous at all real numbers less than 5.
CaseII : c = 5
Then, 
Therefore, f iscontinuous at x = 5
Case III: c >5
Therefore, f iscontinuous at all real numbers greater than 5.
Hence, f iscontinuous at every real number and therefore, it is a continuous function.