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

Question

Explain using the theorems why the function is continuous at every number in its domain. Q(X) = 3 Squareroot x - 3/x^3 - 3 Q(X) is a polynomial, so it is continuous at every number in its domain. Q(X) is a rational function, so it is continuous at every number in its domain. Q(X) is a composition of functions that are continuous, so it is continuous at every number in its domain. Q(X) is not continuous at every number in its domain, none of these State the domain. (Enter your answer using interval notation.)

Explanation / Answer

b) Rational functions are continuous for all real numbers except at those where the denominator is zero. If the denominator of a rational function f(x) is zero at x=a, then it contains some number of factors of (x - a).

Except, at x = (3)^(1/3)

Find the domain by finding where the equation is defined.

Domain: (, (3)^(1/3)((3)^(1/3), ),{x/x(3)^(1/3)}

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