Composing Two Drawn Graphs

Difficulty: Medium · Topics: Algebra, Functions, Composition of Functions

Chizilgan ikki grafikning kompozitsiyasi

The graphs of y=f(x) (purple) and y=g(x) (teal) on -3≤ x≤ 3 are made of straight pieces.

graph "x":[-4,4],"y":[-3,3],"xTicks":[-4,-3,-2,-1,1,2,3,4],"yTicks":[-3,-2,-1,1,2,3],"grid":true,"clip":true,"label":"Two piecewise linear graphs: f in purple and g in teal","items":["type":"line","from":[-3,2],"to":[-1,-2],"start":"closed","type":"line","from":[-1,-2],"to":[1,0],"type":"line","from":[1,0],"to":[3,2],"end":"closed","type":"line","from":[-3,-1],"to":[0,2],"start":"closed","color":"teal","type":"line","from":[0,2],"to":[2,-2],"color":"teal","type":"line","from":[2,-2],"to":[3,1],"end":"closed","color":"teal","type":"label","at":[3.25,2.55],"text":"y = f(x)","anchor":"e","size":13,"type":"label","at":[-3.6,-1.55],"text":"y = g(x)","anchor":"e","size":13,"type":"guide","at":[2,-2],"to":"both","type":"guide","at":[-3,2],"to":"both","type":"guide","at":[-1,-2],"to":"both","type":"guide","at":[0,2],"to":"y"]

Find (f° g)(2)+(g° f)(-3).