# Thread: If a function is continuous

1. ## If a function is continuous

Hello i got problem with nr 22. Because x^(1/3) is delfined for possitive and negative so idk what its domain is.

2. ## Re: If a function is continuous

Originally Posted by Petrus
Hello i got problem with nr 22. Because x^(1/3) is delfined for possitive and negative so idk what its domain is.

The domain of $\sqrt[3]x(x^3+1)$ is all real numbers.

Both factors are continuous functions.

3. ## Re: If a function is continuous

if $\sqrt[3]{a} = x$ then $a = x^3$ or a solution must exist for $x^3 - a = 0$ Now what do you know about cubic roots? It has 3 roots, and complex roots only come in pairs when you have real coefficients, so u could either have 2 complex roots and 1 real root or 3 real roots. Which means you always have atleast one real root, so the domain is all real numbers.