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Thread: Inverse Function Problem

  1. #1
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    Inverse 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 $\displaystyle q$
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  2. #2
    A Plied Mathematician
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    What ideas have you had so far?
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  3. #3
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    $\displaystyle f^{-1}(x) = \frac{2+kx}{23x}$ right?
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  4. #4
    A Plied Mathematician
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    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!
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