Question

Determine the inverse of h(x)=x/x-2

Answer 1

Given:

`h(x)=(x)/(x-2)`

To find the inverse of h(x):

Let the equation be,

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

Swap x and y, we get

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

On solving we get,

`\begin{gathered} (y-2)/(y)=(1)/(x) \\ 1-(2)/(y)=(1)/(x) \\ -(2)/(y)=(1)/(x)-1 \\ -(2)/(y)=(1-x)/(x) \\ (2)/(y)=-((1-x)/(x))_{} \\ (2)/(y)=(x-1)/(x) \\ (2)/(y)=(x-1)/(x) \\ (1)/(y)=(x-1)/(2x) \\ y=(2x)/(x-1) \end{gathered}`

Hence, the inverse of the h(x) is,

`(2x)/(x-1)`