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

Question

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

2x2 ? x ? 5 x2 + 9 Explain, using the theorems, why the function is continuous at every number in its domain. F(x) = 2x2 ? x ? 5 x2 + 9 F(x) is a polynomial, so it is continuous at every number in its domain. F(x) is a rational function, so it is continuous at every number in its domain. F(x) is a composition of functions that are continuous for all real numbers, so it is continuous at every number in its domain. F(x) is not continuous at every number in its domain. none of these State the domain. (Enter your answer using interval notation.)

Explanation / Answer

F(x) = 2x^2 -x -5 is a polynomial so it is continuous

F(x) = x^2 +9 is also a polynomial , it's also continuous

F(x) 2x^2 -x -5 / x^2 +9 is a rational function so its also continuous

the domain in all the three cases is (-infinity , +infinity ) because the function has a real value for every real value of x.

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