## Understanding QuasiLinearity

Hi,

I have two questions.

(1) I am trying to understand how the following function is quasi-linear:

Code:
f = min(1/2,x,x^2)
For it to be quasi linear it has to be quasi convex and quasi concave at same time.

(2) I think the reason the above function is not concave is cause on a certain interval (0,1) f = x^2 which is convex. Am I correct in my reasoning?

Thanks guys
 What is the domain of your function?
 Real numbers R

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## Understanding QuasiLinearity

 Quote by newphysist (1) I am trying to understand how the following function is quasi-linear: Code: f = min(1/2,x,x^2) For it to be quasi linear it has to be quasi convex and quasi concave at same time.
Yes. Which it is.
 (2) I think the reason the above function is not concave is cause on a certain interval (0,1) f = x^2 which is convex. Am I correct in my reasoning?
Yes, though it would be more accurate to observe that on (0, 1/√2) it is not concave. (min{.5, x/2, x} would have been concave.)
 This function is monotonic. And every monotonic function is quasilinear.

 Tags quasi linear