f(x) = x
f(f(f(f(f(f(f(f(f(f(x)))))))))) = ___
[tex]\begin{aligned}&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(x\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\\&{=\ }\boxed{\ \bf x\ }\end{aligned}[/tex]
Pembahasan
Komposisi Fungsi
Diberikan fungsi: [tex]f(x) = x[/tex]
Dengan bentuk fungsi seperti ini, di mana apa yang dipetakan dan hasil pemetaan oleh [tex]f[/tex] adalah identitas, yang juga berakibat pada [tex]f(x)[/tex] memiliki invers [tex]f(x)[/tex] itu sendiri, maka hasil komposisi bersarang (nested) fungsi [tex]f[/tex] hingga berapa kalipun akan menghasilkan [tex]x[/tex] pula.
[tex]\begin{aligned}&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf f\left(x\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\right)\right)\end{aligned}[/tex]
[tex]\begin{aligned}{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(\bf x\right)\right)\right)\end{aligned}[/tex]
[tex]\begin{aligned}{=\ }&f\left(f\left(\bf x\right)\right)\\{=\ }&f\left(\bf x\right)\\{=\ }&\bf x\end{aligned}[/tex]
[tex]\blacksquare[/tex]
[answer.2.content]
