This problem mainly investigates the application of the number of zero points of a function. The combination of numbers and shapes is the key to solve this problem, which is comprehensive and difficult.

F(x)=a|x| is obtained from y=f(x)-a|x|, and a conclusion can be drawn by combining numbers.

Solution: get f(x)=a|x| from y=f(x)-a|x|=0, and make an image with functions y=f(x) and y = a | x |. When a≤0, the condition is not satisfied, so a>0. This is the detailed answer/exercise/math /804202 Known function f(x)=|x? +5x+4|，x≤0？ 2|x-2|, x>0, if the function y=f(x)-a|x| has exactly four zeros, then the value range of the real number a.

Considering the answers carefully, the basis of such questions is still very important. After mastering the basic knowledge, draw inferences from others. When analyzing, don't be confused. I hope it helps you. Come on ~ I hope it's useful and adopt it!