# Understanding QuasiLinearity

by newphysist
Tags: quasi linear
 P: 12 Hi, I have two questions. (1) I am trying to understand how the following function is quasi-linear: 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
 P: 350 What is the domain of your function?
 P: 12 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: 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.)
 P: 350 This function is monotonic. And every monotonic function is quasilinear.

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