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Let $\(f(x) = \displaystyle \frac{1}{ax+b}\)$ where $a$ and $b$ are nonzero constants. Find all solutions to $\(f^{-1}(x) = 0\)$. Express your answer in terms of $a$ and/or $b$.

 Jul 24, 2018
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Let $f(x) = \displaystyle \frac{1}{ax+b}$ where $a$ and $b$ are nonzero constants.
Find all solutions to $f^{-1}(x) = 0$.
Express your answer in terms of $a$ and/or $b$.

 

\(\begin{array}{|rcll|} \hline f\left(f^{-1}(x)\right) &=& x \quad & | \quad f^{-1}(x) = 0 \\\\ f\left(0\right) &=& x \quad & | \quad f(0)=\dfrac{1}{a\cdot 0+b} = \dfrac1b \\\\ \dfrac1b &=& x \\\\ \mathbf{x} & \mathbf{=} & \mathbf{\dfrac1b} \\ \hline \end{array}\)

 

laugh

 Jul 24, 2018

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