Question

How do I solve and what would the answer be?

Answer 1

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

To find the inverse of a function:

`f(x)=(2)/(x-5)`

We will follow the steps below

Step 1: Replace f(x) witth y

`y=(2)/(x-5)`

Step 2: interchange x with y

`x=(2)/(y-5)`

Step 3: Make y the subject of the formula

`\begin{gathered} y-5=(2)/(x) \\ \\ y=(2)/(x)+5 \end{gathered}`

Thus, the inverse of the function is:

`y=(2)/(x)+5`