Explain, using theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. f(x) = (2x² - x - 1)/(x² + 1).

a) f(x) is continuous at every number in its domain because it's a rational function with no asymptotes. The domain is all real numbers.
b) f(x) is continuous at every number in its domain due to the polynomial function in the numerator and denominator. The domain is R except for x = ±i.
c) f(x) is continuous at every number in its domain as it satisfies the conditions of theorem 4, 5, 7, and 9. The domain is all real numbers.
d) f(x) is not continuous at every number in its domain due to the division by zero at x = 0. The domain is R excluding x = 0.