Is the following fractional function convex?

Question

Is $\displaystyle f(x_1,x_2) = x_1 - \frac{1}{x_2}$ a convex function? What if we restrict the values of this function to the positive reals?

Answer 1

It is convex for $x_2 < 0$, not for $x_2 > 0$ (there it is concave).