Let \(f(x)=3x-2\), and let \(g(x)=f(f(f(f(x))))\). If the domain of \(g\) is \(0\leq x\leq 2\), compute the range of \(g\).
+487 First, let's solve for $g(x)$. We have $g(x)=f(f(f(f(x))))=f(f(f(3x-2)))=f(f(3(3x-2)-2=9x-8))=f(3(9x-8)-2=27x-26)=3(27x-26)-2=81x-80$.
So, the lower range is $81(0)-80=-80$.
Also, the upper range is $81(2)-80=82$.
So, the range is $\boxed{[-80, 82]}$, or $\boxed{-80 \leq y \leq 82}$
+487 First, let's solve for $g(x)$. We have $g(x)=f(f(f(f(x))))=f(f(f(3x-2)))=f(f(3(3x-2)-2=9x-8))=f(3(9x-8)-2=27x-26)=3(27x-26)-2=81x-80$.
So, the lower range is $81(0)-80=-80$.
Also, the upper range is $81(2)-80=82$.
So, the range is $\boxed{[-80, 82]}$, or $\boxed{-80 \leq y \leq 82}$
