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Define f(x)=3x-8. If f^{-1} is the inverse of f, find the value(s) of x for which f(x)=f^{-1}(x).

 Nov 6, 2019

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 #1
avatar+23862 
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Define \(f(x)=3x-8\).

If \(f^{-1} \)is the inverse of \(f\), find the value(s) of \(x\) for which \(f(x)=f^{-1}(x)\).

 

\(\begin{array}{|rcll|} \hline \mathbf{f(x)}&=& \mathbf{3x-8} \\\\ x &=& 3 f^{-1}(x)-8 \quad & | \quad \mathbf{f^{-1}(x)=f(x)} \\ x &=& 3 f(x)-8 \quad & | \quad \mathbf{f(x)=3x-8} \\ x &=& 3 (3x-8)-8 \\ x &=& 9x-24-8 \\ 8x &=& 32 \\ x &=& \dfrac{32}{8} \\ \mathbf{ x } &=& \mathbf{4} \\ \hline \end{array} \)

 

laugh

 Nov 6, 2019
 #1
avatar+23862 
+1
Best Answer

Define \(f(x)=3x-8\).

If \(f^{-1} \)is the inverse of \(f\), find the value(s) of \(x\) for which \(f(x)=f^{-1}(x)\).

 

\(\begin{array}{|rcll|} \hline \mathbf{f(x)}&=& \mathbf{3x-8} \\\\ x &=& 3 f^{-1}(x)-8 \quad & | \quad \mathbf{f^{-1}(x)=f(x)} \\ x &=& 3 f(x)-8 \quad & | \quad \mathbf{f(x)=3x-8} \\ x &=& 3 (3x-8)-8 \\ x &=& 9x-24-8 \\ 8x &=& 32 \\ x &=& \dfrac{32}{8} \\ \mathbf{ x } &=& \mathbf{4} \\ \hline \end{array} \)

 

laugh

heureka Nov 6, 2019

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