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I have a function: u(x)= x_1 + x_2 + min{x_1, x_2) $ u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if itsit's convex or not? Also, what would be the general way to show if any given function is convex.

I have a function: u(x)= x_1 + x_2 + min{x_1, x_2). How do we algebraically show if its convex or not? Also, what would be the general way to show if any given function is convex.

I have a function: $ u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.

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Algebraic approach towards convexity

I have a function: u(x)= x_1 + x_2 + min{x_1, x_2). How do we algebraically show if its convex or not? Also, what would be the general way to show if any given function is convex.