Step 1

The function .

Since the degree of the numerator and the denominator of the function is same, the function is a improper polynomial function.

Domain:

The domain of a function is for all values of x, which makes the function mathematically correct.

Since there shouldn\\'t be any zero in denominator.

The denominator expression is always greater than one. \ \

,for all  values of x.

So the domain of any polynomial function  .

Any polynomial function is continuous on its domain.

Thus the function is continuous at every number on  .

is a rational function, so it is continuous at every number in its domain.

Solution:

Option (b) is correct choice.

is a rational function, so it is continuous at every number in its domain.