calculus - Use the Intermediate Value Theorem to show that $cos(x)=x^3$ has a solution.

I am not sure if I am fully understanding how to solve this, but I think that, since the since $g(x)=\cos(x)$ and $g(x)=x^3$ are continuous everywhere, the function $f(x)=\cos(x)-x^3$ must also be continuous everywhere, and therefore, according to the Intermediate Value Theorem, $\cos(x)=x^3$ must have a solution. However, I'm not sure if that's true.

How can I show that $\cos(x)=x^3$ has a solution?