To find the inverse of a function:
[tex]f(x)=\frac{2}{x-5}[/tex]We will follow the steps below
Step 1: Replace f(x) witth y
[tex]y=\frac{2}{x-5}[/tex]Step 2: interchange x with y
[tex]x=\frac{2}{y-5}[/tex]Step 3: Make y the subject of the formula
[tex]\begin{gathered} y-5=\frac{2}{x} \\ \\ y=\frac{2}{x}+5 \end{gathered}[/tex]Thus, the inverse of the function is:
[tex]y=\frac{2}{x}+5[/tex]