# Let R={0,1,2,3} be the range of h(x) = x-7, then what is the domain of h?

Aug 19, 2017

See a solution process below:

#### Explanation:

The range is the output of a function. To find the domain, the input to a function, we need to find the value of $x$ for each value of the Range.

For $\ast R = 0 \ast$

$0 = x - 7$
$0 + \textcolor{red}{7} = x - 7 + \textcolor{red}{7}$
$7 = x - 0$
$7 = x$
$x = 7$

For $\ast R = 1 \ast$

$1 = x - 7$
$1 + \textcolor{red}{7} = x - 7 + \textcolor{red}{7}$
$8 = x - 0$
$8 = x$
$x = 8$

For $\ast R = 2 \ast$

$2 = x - 7$
$2 + \textcolor{red}{7} = x - 7 + \textcolor{red}{7}$
$9 = x - 0$
$9 = x$
$x = 9$

For $\ast R = 3 \ast$

$3 = x - 7$
$3 + \textcolor{red}{7} = x - 7 + \textcolor{red}{7}$
$10 = x - 0$
$10 = x$
$x = 10$

The Domain Is: $D = \left\{7 , 8 , 9 , 10\right\}$