Math Help - Concave function and little-oh

The problem is:

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?

Originally Posted by batman

The problem is:

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 .

The function you mention is strictly concave, but nog strongly concave. Thank you anyway.

Originally Posted by batman

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.