Inverse of Cosine

Geometry Level 2

Let \(g(x)\) be the inverse function of \(f(x)=\cos x\ (0 < x < \pi)\) such that \[g\left(\frac{5}{13}\right)=\alpha, g\left(\frac{12}{13}\right)=\beta.\] What is the value of \(f(\alpha+\beta)?\)

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