f(|x|) and |f(x)| from One Graph

Difficulty: Hard · Topics: Algebra, Functions, Graphs of Functions

Bitta grafikdan f(|x|) va |f(x)|

The graph of y=f(x) on -4≤ x≤ 4 is made of straight pieces.

graph "x":[-5,5],"y":[-3,4],"xTicks":[-5,-4,-3,-2,-1,1,2,3,4,5],"yTicks":[-3,-2,-1,1,2,3,4],"grid":true,"clip":true,"label":"Graph of y = f(x) made of four straight pieces on -4 ≤ x ≤ 4","items":["type":"line","from":[-4,2],"to":[-2,-2],"start":"closed","type":"line","from":[-2,-2],"to":[0,1],"type":"line","from":[0,1],"to":[2,3],"type":"line","from":[2,3],"to":[4,-1],"end":"closed","type":"guide","at":[-2,-2],"to":"both","type":"guide","at":[0,1],"to":"both","type":"guide","at":[2,3],"to":"both","type":"guide","at":[-4,2],"to":"both","type":"guide","at":[4,-1],"to":"both"]

Let a be the number of solutions of f(lvert xrvert)=1, and b the number of solutions of lvert f(x)rvert=2. Find a+b.