(a) The given function is

Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.

Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.

Therefore, f is continuous at all real numbers less than 5. Case II : 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.