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# What is range of $f(x)=^{7-x}P_{x-3}$

$\begin{array}{1 1} \{1,2,3,4,5,6\} \\ \{1,2,3,4,5\} \\ \{1,2,3\} \\ \{3,4,5\} \end{array}$

$f(x)=\large^{7-x}P_{x-3}$
$x\in Z,\:\:7-x\geq 0,\:\:x-3\geq 0\:\:and\:\:7-x\geq x-3$
$\Rightarrow x\leq 7,\:\:x\leq 5\:\:and\: x\geq 3$
$\Rightarrow\:x\in \{3,4,5\}$ That is $domain =\{3,4,5\}$
when $x=3. \:f(x)=f(3)=1$
When $x=4,\:f(x)=f(4)=3$
When $x=5,\:f(x)=f(5)=2$
$\Rightarrow \:Range=\{1,2,3\}$