Numerical Root-finding Algorithms for Continous Piecewise Functions

Question

I have this function: $$f(x)=10^4(\sin^2(\frac{33}{x} \pi)+\sin^2(x\pi))$$ $$g(x)=\begin{cases}f(x)<10:f(x)\\f(x) \geq 10:10 \end{cases}$$ How would I find a root of $g(x)$, given I have an interval where only one root must be? Is there a way to figure out if any value is below 10 in any interval?

Answer 1

$g(x)\ge10$ so that $g$ has no root.

Answer 2

If you have a bound on the root, you can use the bisection method. For more information about the bisection method, you can look here: Wikipedia Article on bisection method However, it does not use integration.

Bob