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?

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