# How do you find values of x for which the function g(x) = (sin(x^20+5) )^{1/3} is continuous?

The function is continuous for every x in $\left(- \infty , + \infty\right)$.
${x}^{20} + 5$ is a polynomial, and so it is continuous everywhere;
$\sin f \left(x\right)$ is continuous however $f \left(x\right)$ is continuous;
${\left(h \left(x\right)\right)}^{\frac{1}{3}}$ is continuous howerver $h \left(x\right)$ is continuous, and so the solution.