Let $f(x)=x+1$ and $g(x)=2x$.  Also denote the inverses to these functions as $f^{-1}$ and $g^{-1}$.  Compute \[f(g^{-1}(f^{-1}(f^{-1}(g(f(5)))))).\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $f(x)=x+1$ and $g(x)=2x$.  Also denote the inverses to these functions as $f^{-1}$ and $g^{-1}$.  Compute \[f(g^{-1}(f^{-1}(f^{-1}(g(f(5)))))).\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
Let $f(x)=x+1$ and $g(x)=2x$.  Also denote the inverses to these functions as $f^{-1}$ and $g^{-1}$.  Compute \[f(g^{-1}(f^{-1}(f^{-1}(g(f(5)))))).\]
train