You can draw a picture, which is 3/2x+ 1/2, -x+3.

Take the minimum value at the intersection.

Wrong topic, I personally think such a topic is the combination of numbers and shapes.

If the numbers are not combined, even if -x+3≥3/2x+ 1/2, the range of such x is complicated.

The combination of numbers and shapes is very fast, which is an important method to do math problems. You must be able to use it.

This is a function image first, and then it is easy to understand. F(x) takes the maximum value of the three functions, that is, the top line is taken after the images of the three functions intersect.

Then solve the problem that the intersection of f(x)=-x+3 and f (x) = x 2-4x+3 is (0,3) and (3,0).

These two intersections are on the x axis and the y axis. First, solve the intersection of these two functions. When x

The intersection of the resolvent formula f(x)=3/2x+ 1/2 and f(x)=-x+3 is (1, 5/2), f(x)=3/2x+ 1 and f (x) = x 2-.

The minimum value of the third intersection of (1, 2) and the domain y of the previous partition function is that the intersection is (1, 5/2), so the minimum value is 2.

Think about it.