Question: How to determine the concavity of an unknown function?

Suppose we have an unknown parametric function like g(x). We do not know the exact form but we know that g(x) is increasing and concave. Also, we define h(x) = g(x)*f(x) where we know the exact form of f(x) like f(x)=2x+5. Here, I want to investigate if the function h(x) is concave or not. How is it possible to do this?



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