# 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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