Answer :

[tex]\mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)\: [/tex]

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]