Problem 19

Given information

The given function is   

Theorem 4 and 7, where theorem 4 states that the sum of two continuous functions is continuous and theorem 7 states that the root and polynomial functions are both continuous on its domain.

Step-by-step explanation

The given function is    

Let   and  

So,  

Since  is a polynomial function, it is continuous in its domain and is a root function, so, it is continuous in its domain.

Now is well defined when

So, the domain of is

Thus,  is continuous in its domain  by theorems 4 and 7.