Composing a Function and Its Inverse
Difficulty: Medium · Topics: Discrete Mathematics, Functions, Inverse Functions
Funksiya va uning teskarisini kompozitsiyalash
For the set X=\1,2,3,4,5\, the graph of a function f from X to X is shown below.
graph "x":[-0.4,5.8],"y":[-0.4,5.8],"xTicks":[1,2,3,4,5],"yTicks":[1,2,3,4,5],"label":"Five points of a function on 1,2,3,4,5: (1,2), (2,1), (3,4), (4,5), (5,3)","items":["type":"point","at":[1,2],"type":"point","at":[2,1],"type":"point","at":[3,4],"type":"point","at":[4,5],"type":"point","at":[5,3]]
Find the value of b satisfying (f° f)(a)=3 and ≤ft(f^-1° f^-1 )(a)=b.
X=\1,2,3,4,5\ to‘plam uchun X dan X ga f funksiyaning grafigi quyida ko‘rsatilgan.
graph "x":[-0.4,5.8],"y":[-0.4,5.8],"xTicks":[1,2,3,4,5],"yTicks":[1,2,3,4,5],"label":"Five points of a function on 1,2,3,4,5: (1,2), (2,1), (3,4), (4,5), (5,3)","items":["type":"point","at":[1,2],"type":"point","at":[2,1],"type":"point","at":[3,4],"type":"point","at":[4,5],"type":"point","at":[5,3]]
(f° f)(a)=3 va ≤ft(f^-1° f^-1 )(a)=b ni qanoatlantiruvchi b ning qiymatini toping.