Question

How do I solve and what would the answer be?

Answer 1

Given:

The function is given as,

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

The objective is to find the inverse function.

Step-by-step explanation:

The given expression can be written as,

`y=(2)/(x-5)\text{ . . . . . (1)}`

The inverse of a function can be calculated by interchanging the x and y variables in equation (1).

`x=(2)/(y-5)\text{ . . . . . (2)}`

Now, solve for y in equation (2).

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

Hence, the inverse function is y = (2/x) + 5.