Let $f(x)=x+1$ and $g(x)=2x$.  Also denote the inverses to these functions as $f^{-1}$ and $g^{-1}$.  Compute \[f(g^{-1}(f^{-1}(f^{-1}(g(f(5)))))).\]
Question:
Let $f(x)=x+1$ and $g(x)=2x$.  Also denote the inverses to these functions as $f^{-1}$ and $g^{-1}$.  Compute \[f(g^{-1}(f^{-1}(f^{-1}(g(f(5)))))).\]
Answer:
Let's think step by step.

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