Question

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

Answer 1

The function is continuous for every x in `(-oo,+oo)`.

This is because:

`x^20+5` is a polynomial, and so it is continuous everywhere;

`sinf(x)` is continuous however `f(x)` is continuous;

`(h(x))^(1/3)` is continuous howerver `h(x)` is continuous, and so the solution.