Any body knows how to prove convexity of this function? $$f(x_1,x_2,x_3)=\frac{1}{x_1-\frac{1}{x_2-\frac{1}{x_3}}}$$ for $$x_i>0$$
Update: It seems this homework question is not right. As @user854214 said in comments in some points the function is not defined.