Given the function $\displaystyle f(x) = \frac{2}{23x - k} , x \neq \frac{k}{3}$ and $\displaystyle f^{-1}(x) = \frac{q}{x} + \frac{5}{3} ,x \neq 0$.Find the value of $\displaystyle k$ and $\displaystyle q$

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- Nov 8th 2010, 04:32 AMmastermin346Inverse Function Problem
Given the function $\displaystyle f(x) = \frac{2}{23x - k} , x \neq \frac{k}{3}$ and $\displaystyle f^{-1}(x) = \frac{q}{x} + \frac{5}{3} ,x \neq 0$.Find the value of $\displaystyle k$ and $\displaystyle q$

- Nov 8th 2010, 04:49 AMAckbeet
What ideas have you had so far?

- Nov 8th 2010, 05:11 AMmastermin346
$\displaystyle f^{-1}(x) = \frac{2+kx}{23x}$ right?

- Nov 8th 2010, 05:22 AMAckbeet
Incidentally, I have a comment: either

$\displaystyle f(x)=\dfrac{2}{3x-k},$ with $\displaystyle x\not=k/3,$ or

$\displaystyle f(x)=\dfrac{2}{23x-k},$ with $\displaystyle x\not=k/23.$ Which is it?

Let's nail down the exact problem first, before we waste a lot of time solving a different problem from the one you need to solve!