Question

What is the range of the function `y=(x+5)/(x-2)`?

Answer 1

`(-oo,1)(1,oo)`

Explanation:

Solve for `x`, as follows

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

`yx -x= 2y+5`

`x(y-1)=2y+5`

`x= (2y+5)/(y-1)`

In the above expression, `x` becomes undefined for `y=1`. This except for `y=1`, `x` is defined on all the number line. Hence Range of `y` is `(-oo,1)U(1,oo)`