Question

How do you find the domain and range of `f(x)=(x+2)/(x-2)`?

Answer 1

The domain of `f(x)` is `RR-{2}`
The range of `f(x)` is `RR-{1}`

Explanation:

As we cannot divide by `0`, `x!=2`

The domain of `f(x)` is `D_f(x)=RR-{2}`

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

Then,

`yx-2y=x+2`

`yx-x=2y+2`

`x(y-1)=2(y+1)`

`x=2(y+1)/(y-1)`

Therefore,

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

The domain of `x` is the range of `y`

The range of `f(x)` is `R_f(x)=RR-{1}`

graph{(y-(x+2)/(x-2))(y-1)=0 [-9.25, 10.75, -2.93, 7.07]}