How to prove that f(x) is convex?
For all $$x_i>0$$ we have $$ f(x) = \frac{1}{x_1 - \frac{1}{ x_2 - \frac{1}{x_3} }} $$ I tried to take the second derivative (hessian matrix) but it was too long and i couldn't prove that the hessian is PSD. Also tried the Jensen's inequality, but again, couldn't go with it. So, is there a simpler way to prove this function's convexity? Is this a linear fractional function? If so, then how would it be related to convexity? (Thank you in advance.)