Given the function:
[tex]f(x)\text{ = }\frac{2}{x\text{ - 5}}[/tex]
To find the inverse function:
1. Invert the variables, as follows:
[tex]x\text{ = }\frac{2}{y-5}[/tex]
2. Solve for y:
[tex]\begin{gathered} x\text{ = }\frac{2}{y-5} \\ \\ y-5=\frac{2}{x} \\ \\ f^{-1}(x)\text{ = }\frac{2+5x}{x} \end{gathered}[/tex]
