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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.

 Mar 10, 2020
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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.

 

I am not very comfortable with these but this is what I get.

 

\(f(x)=3x-2 \quad \{0\le x\le2\}\\ ff(x)=9x-8 \quad \{-2\le x\le4\}\\ fff(x)=27x-26 \quad \{-26\le x\le 28\}\\ ffff(x)=81x-80 \quad \{-728\le x\le 730\}\\\)

When x=-728   g(x)=ffff(x)= -59048

When x=730   g(x)=ffff(x)= 59050

 

So the range of g is     [-59048,59050]

 Mar 11, 2020

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