Thread: 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 $\displaystyle q$

What ideas have you had so far?

$\displaystyle f^{-1}(x) = \frac{2+kx}{23x}$ right?

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!