Question

How do I solve and what would the answer be?

Answer 1

Given the function below

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

The inverse of the function is denoted by

`f^(-1)(x)_{}`

It can be obtained through the process below

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

Swap the position of y and x in the equation above

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

Solve for y in the resulting equation from the swap

`\begin{gathered} By\text{ cross multiplying} \\ x(y-5)=2 \\ \text{Divide both sides by x} \\ (x(y-5))/(x)=(2)/(x) \end{gathered}`
`\begin{gathered} y-5=(2)/(x) \\ \text{Add -5 to both sides} \\ y-5+5=(2)/(x)+5 \end{gathered}`
`y=(2)/(x)+5`

Hence, the inverse of f(x) is

`f^(-1)(x)=(2)/(x)+5`