Question

Explain, using Theorems why the function is continuous at every number in its domain. State the domain.

F (x) = (2x² - x - 1)/(x² + 1)

Answer 1

Step 1:

The function .

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

Domain of any polynomial function .

From theorem 5, any polynomial function is continuous on its domain.

Thus the function is continuous at every number on  .

Solution:

The function is continuous on .