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A change machine lets you put in an $x$ -dollar bill, and gives you $f(x)$ nickels in return equal in value to $x$ dollars. Any current, legal denomination of US paper money can be fed to the change machine. What is the domain of $f\text{?}$

Solution

The current, legal denominations of US paper money are $\$1\text{,}$ $\$2\text{,}$ $\$5\text{,}$ $\$10\text{,}$ $\$20\text{,}$ $\$50\text{,}$ and $\$100\text{.}$ So the domain of $f$ is the set $\{1,2,5,10,20,50,100\}\text{.}$