KUIS YUK f(x) = x f(f(f(f(f(f(f(f(f(f(x)))))))))) = __

May 2022 1 31 Report

KUIS YUK
f(x) = x
f(f(f(f(f(f(f(f(f(f(x)))))))))) = ___

$\begin{aligned}&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(x\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\\&{=\ }\boxed{\ \bf x\ }\end{aligned}$

Pembahasan

Komposisi Fungsi

Diberikan fungsi: $f(x) = x$

Dengan bentuk fungsi seperti ini, di mana apa yang dipetakan dan hasil pemetaan oleh $f$ adalah identitas, yang juga berakibat pada $f(x)$ memiliki invers $f(x)$ itu sendiri, maka hasil komposisi bersarang (nested) fungsi $f$ hingga berapa kalipun akan menghasilkan $x$ pula.

$\begin{aligned}&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf f\left(x\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\right)\right)\end{aligned}$
$\begin{aligned}{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(f\left(\bf x\right)\right)\right)\right)\\{=\ }&f\left(f\left(f\left(\bf x\right)\right)\right)\end{aligned}$
$\begin{aligned}{=\ }&f\left(f\left(\bf x\right)\right)\\{=\ }&f\left(\bf x\right)\\{=\ }&\bf x\end{aligned}$