Following the Arrows Twice

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

Strelkalar bo‘ylab ikki marta

The diagrams show g:X→ Y and f:Y→ Z.

graph "x":[-5.7,5.7],"y":[-2.975,3.575],"axes":false,"label":"Arrow diagrams of g and f","items":["type":"ellipse","at":[-4.4,0],"rx":0.95,"ry":2.725,"ink":true,"width":1.4,"type":"label","at":[-4.4,3.125],"text":"X","size":17,"type":"ellipse","at":[0,0],"rx":0.95,"ry":2.725,"ink":true,"width":1.4,"type":"label","at":[0,3.125],"text":"Y","size":17,"type":"ellipse","at":[4.4,0],"rx":0.95,"ry":2.725,"ink":true,"width":1.4,"type":"label","at":[4.4,3.125],"text":"Z","size":17,"type":"label","at":[-2.2,2.875],"text":"g","size":17,"type":"label","at":[2.2,2.875],"text":"f","size":17,"type":"label","at":[-4.4,1.05],"text":"1","size":16,"italic":false,"type":"label","at":[-4.4,-0.2],"text":"2","size":16,"italic":false,"type":"label","at":[-4.4,-1.45],"text":"3","size":16,"italic":false,"type":"label","at":[0,1.675],"text":"a","size":16,"type":"label","at":[0,0.425],"text":"b","size":16,"type":"label","at":[0,-0.825],"text":"c","size":16,"type":"label","at":[0,-2.075],"text":"d","size":16,"type":"label","at":[4.4,1.05],"text":"4","size":16,"italic":false,"type":"label","at":[4.4,-0.2],"text":"5","size":16,"italic":false,"type":"label","at":[4.4,-1.45],"text":"6","size":16,"italic":false,"type":"vector","from":[-4.05,1.25],"to":[-0.35,0.625],"ink":false,"width":1.6,"type":"vector","from":[-4.05,0],"to":[-0.35,-1.875],"ink":false,"width":1.6,"type":"vector","from":[-4.05,-1.25],"to":[-0.35,0.625],"ink":false,"width":1.6,"type":"vector","from":[0.35,1.875],"to":[4.05,-1.25],"color":"teal","ink":false,"width":1.6,"type":"vector","from":[0.35,0.625],"to":[4.05,1.25],"color":"teal","ink":false,"width":1.6,"type":"vector","from":[0.35,-0.625],"to":[4.05,0],"color":"teal","ink":false,"width":1.6,"type":"vector","from":[0.35,-1.875],"to":[4.05,-1.25],"color":"teal","ink":false,"width":1.6]

Find the sum of all elements in the range of f° g.