The two functions given in the problem are exactly the inverse functions of each other, so finding the shortest distance is actually twice the shortest distance from the first function to y=x (the images of the original function and the inverse function are symmetrical about y=x). Let the coordinate of the point on the first function be (x, e x/2), and use the distance formula from the point to the straight line to find (x, e x/2) to x-Y. Then g' (x) = 1-e x/2, and when g'(x)=0, x=ln2. When x=ln2, take the minimum value and return x=ln2 to | x-e x/2 |/√ 2 = (1-LN2).