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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

#1
+24430
+1

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

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

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

Nov 6, 2019

#1
+24430
+1

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

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

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

heureka Nov 6, 2019