The function $f \colon \mathbb R - {2} \to \mathbb R \setminus \{5\}$ defined by $ f(x) =\frac{ (5x+1)} {x-2} $ is bijective. Determine its inverse function.
I have no idea how to do this problem. The way I go about such problems is usually, find the inverse $(f^{-1} (x))$ and plugging it into $f(x) $ to show that it equals $x$, therefore it is bijective.
I am not really sure on how to find the inverse in this one because I cannot use partial fractions in this. Even a starting point would be helpful!
The usual way to do this is to write $x=\frac{5y+1}{y-2}$, and then solve for $y$.
However, given what you know about the domain and range, you might guess that the answer is of the form $\frac{2x+k}{x-5}$, then write down the equation $f(f^{-1}(x))=x$ and solve for k.