①    The peak widths at half height are straightforwardly found, just as 2 x the positive intercepts on the line F(x) = 0.5:

kmax : 0.5 1.0 2.0 5.0

x: 2.80 1.40 0.70 0.28

Δx½: 5.60 2.80 1.40 0.56

②    Looking at these numbers, you can readily see that, for example, when kmax  is doubled, Δx½  halves:  there appears to be a reciprocal relationship. This is confirmed by plotting 1/Δx½  against kmax :

From the gradient of the graph, we can quantify this relationship as:   1/Δx½     =   0.71 kmax

and hence:  Δx½   =  1 / 0.71kmax  =  1.4 / kmax