How do you find the domain and range of $y = (x + 3) / (x -5)$ ?

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Answer 1 · 2017-06-09T15:16:53

The domain is $x in (-oo,5)uu(5,+oo)$
So, the range is $y in (-oo,1)uu(1,+oo)$

As you cannot divide by $0$ , $x!=5$

The domain of $y$ is $x in (-oo,5)uu(5,+oo)$

To find the range, we need $y^-1$

$y=(x+3)/(x-5)$

Interchange $y$ and $x$

$x=(y+3)/(y-5)$

Express $y$ in terms of $x$

$(y-5)x=y+3$

$xy-5x=y+3$

$y(x-1)=5x+3$

$y=(5x+3)/(x-1)$

This is $y^-1$

The domain of $y^-1$ is the range of $y$

So, the range is $y in (-oo,1)uu(1,+oo)$

How do you find the domain and range of y = (x + 3) / (x -5) y = (x + 3) / (x -5)?