Suppose f(x) is a strictly concave function. Prove that x=o(f^(-1)(x)).
Do you have any suggestions on how to prove this?
Do you mean as , or as , or something else?
In any case, I don't think that this result can be true without some additional conditions. For example, the function is strictly concave on the interval , but as
Sorry, I didn't copy the exercise properly from the blackboard. It should have been:
Suppose is strongly concave. Then, as .
That certainly makes a difference, but I still don't understand what's going on here. As far as I can see, a strongly concave function has to be bounded above, so will not exist when x is large.