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

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Answer 1 · 2018-05-20T17:13:16

The domain is $x in (-oo,3)uu(3,+oo)$ . The range is $y in (-oo,0)uu(0,+oo)$

The denominator must be $!=0$

Therefore,

$x-3!=$

$=>$ , $x!=3$

The domain is $x in (-oo,3)uu(3,+oo)$

To find the range, proceed as follows :

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

$y(x-3)=5$

$yx-3y=5$

$yx=5+3y$

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

The denominator is $!=0$

$y!=0$

The range is $y in (-oo,0)uu(0,+oo)$

graph{5/(x-3) [-18.02, 18.02, -9.01, 9.02]}

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