Explain, using the theorems, why the function is continuous at every number in i

Question

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

F(x) = (2x^2-x-4)/(x^2+4)

Choose one of the following choices

A. F(x) is a polynomial, so it is continuous at every number in its domain.

B. F(x) is a rational function, so it is continuous at every number in its domain.

C. F(x) is a composition of functions that are continuous for all real numbers, so it is continuous at every number in its domain.

D. F(x) is not continuous at every number in its domain.

E. None of these

State the domain. (Enter your answer using interval notation.)

Explanation / Answer

The answer is E, but the function is continuous at every number in its domain. The other choices just don't give the correct reasons. Domain: (-infinity, infinity)

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