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\(Suppose that $f(x)=4x+5$. What is $f^{-1}(f^{-1}(9))$?\)

 Jul 28, 2020
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Suppose that \(f(x)=4x+5\).

What is \(f^{-1}\left(f^{-1}(9)\right)\)?

 

\(\begin{array}{|rcll|} \hline \mathbf{f(x)} &=& \mathbf{4x+5} \quad | \quad \text{change } f(x) \text{ and } x \\\\ x &=& 4f^{-1}(x)+5 \quad | \quad x=9 \\ 9 &=& 4f^{-1}(9)+5 \\ 4 &=& 4f^{-1}(9) \\ \mathbf{f^{-1}(9)} &=& \mathbf{1} \\\\ x &=& 4f^{-1}(x)+5 \quad | \quad x=1 \\ 1 &=& 4f^{-1}(1)+5 \\ -4 &=& 4f^{-1}(1) \\ \mathbf{f^{-1}(1)} &=& \mathbf{-1} \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline && \mathbf{f^{-1}\left(f^{-1}(9)\right)} \quad &| \quad \mathbf{f^{-1}(9)=1} \\ &=& f^{-1} (1) \quad &| \quad \mathbf{f^{-1}(1)=-1} \\ &=& \mathbf{-1}\\ \hline \end{array}\)

 

laugh

 Jul 28, 2020

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