Question

How do you find the domain and range of `y=(2x)/(-x-5)`?

Answer 1

The domain of `y` is `RR-{-5}`
The range of `y` is `RR-{-2}`

Explanation:

As you cannot divide by `0`, `-x-5!=0`

The domain of `y` is `D_y=RR-{-5}`

To find the range, we need `f^-1(x)`

`y=2x/-x-5`

`-yx-5y=2x`

`2x+yx=-5y`

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

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

Therefore,

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

The range of `f(x)` is the domain of `f^-1(x)`

The range of `f(x)` is `R_y=RR-{-2}`