\[x = \sqrt[5]{{9 - 11y}}\]

\[\begin{align*}x & = \sqrt[5]{{9 - 11y}}\\ {x^5} & = 9 - 11y\\ & {x^5} - 9 = - 11y\\ y &= - \frac{1}{{11}}\left( {{x^5} - 9} \right)\hspace{0.25in}\hspace{0.25in}\,\,\,\, \to \hspace{0.25in}\hspace{0.25in}\require{bbox} \bbox[2pt,border:1px solid black]{{{W^{ - 1}}\left( x \right) = \frac{1}{{11}}\left( {9 - {x^5}} \right)}}\end{align*}\]

E'tibor bering, biz minus belgisini qavs ichiga ko'paytirdik. Agar minus belgisi oldinda qolsa, uni yo'qotmaslik uchun buni qildik. Buning teskarisini olish uchun buni qilish shart emas.

Va nihoyat, ishimizni tekshirish uchun \(\left( {W \circ {W^{ - 1}}} \right)\left( x \right)\) yoki \(\left( {{W^{ - 1}} \circ W} \right)\left( x \right)\) hisoblang.

Ikkala kompozitsiya ham bajarilishi mumkin, keling, bu holda \(\left( {{W^{ - 1}} \circ W} \right)\left( x \right)\) ni bajaraylik.

\[\begin{align*}\left( {{W^{ - 1}} \circ W} \right)\left( x \right) & = {W^{ - 1}}\left[ {W\left( x \right)} \right]\\ & = \frac{1}{{11}}\left( {9 - {{\left[ {\sqrt[5]{{9 - 11x}}} \right]}^5}} \right)\\ & = \frac{1}{{11}}\left( {9 - \left[ {9 - 11x} \right]} \right)\\ & = \frac{1}{{11}}\left( {11x} \right)\\ & = x\end{align*}\]

Shunday qilib, biz \(x\)-ni kompozitsiyadan chiqardik va shuning uchun biz o'z ishimizni to'g'ri bajarganimizni bilamiz.