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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 $$g$$.

Apr 6, 2021

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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 $\boxed{-80 \leq y \leq 82}$

Apr 6, 2021

#1
+485
+1

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 $\boxed{-80 \leq y \leq 82}$

RiemannIntegralzzz Apr 6, 2021