Exercise 20 Page 638

We will determine whether the inverse of $\frac{3}{x+5}$ is a function. Then, we will find this inverse.

Is the Inverse a Function?

To determine whether the inverse of a function is also a function, we will use the Horizontal Line Test. To do this, we will first make a table of values to graph the given function. When making a table of values, make sure to use a variety of points, including negative and positive values.

$x$	$\frac{3}{x+5}$	$f(x)=\frac{3}{x+5}$
$\text{-}8$	$\frac{3}{\text{-}8+5}$	$\text{-}1$
$\text{-}6$	$\frac{3}{\text{-}6+5}$	$\text{-}3$
$\text{-}5$	$\frac{3}{\text{-}5+5}$	-
$\text{-}4$	$\frac{3}{\text{-}4+5}$	$3$
$\text{-}2$	$\frac{3}{\text{-}2+5}$	$1$
$0$	$\frac{3}{0+5}$	$0.6$
$1$	$\frac{3}{1+5}$	$0.5$

Now, we can plot the obtained points and connect them with a smooth curve. Consider also that for $x=\text{-}5,$ there is a zero in the denominator. Therefore, $\text{-}5$ does not belong to the domain. We will mark it on the graph by drawing a dashed line.