Check for concavity, quasi-concavity with given value of function
First look at the shape of the indifference curves. (I assume that $f$ is a utility function here.) The better-sets are convex, so this is consistent with quasi-concavity of the function $f$.

Second, consider the convex combination $(2,2)=\frac{1}{2}(1,1)+\frac{1}{2}(3,3)$. You have $f(2,2)=2$, but $\frac{1}{2}f(1,1)+\frac{1}{2}f(3,3)=\frac{1}{2}1+\frac{1}{2}4=2.5&gt;2$, which is inconsistent with the function being concave.