Задача №1007
Условие
\(\varphi(t)=t^3+1\). Найти \(\varphi\left(t^2\right)\) и \(\left(\varphi(t)\right)^2\).
Решение
\[
\begin{aligned}
& \varphi\left(t^2\right) = \left(t^2\right)^3+1=t^6+1;\\
& \left(\varphi(t)\right)^2 = \left(t^3+1\right)^2=t^6+2t^3+1.
\end{aligned}
\]
Ответ:
\( \begin{aligned} & \varphi\left(t^2\right) =t^6+1;\\ & \left(\varphi(t)\right)^2 =t^6+2t^3+1. \end{aligned} \)