Question

The range of the function $f(x)={}^{7-x}{P}_{x-3}$ is

• A. $\{1,2,3,4\}$
• B. $\{1,2,3,4,5,6\}$
• C. $\{1,2,3\}$
• D. $\{1,2,3,4,5\}$

Answer 1

Answer: (C)

$7-x\ge 1,x-3\ge 0$
$\text{ and }7-x\ge x-3$
$\Rightarrow x\le 6,x\ge 3,x\le 5$
$\text{ Thus }3\le x\le 5$
$\therefore \text{ Range }=\left\{4P_0,3P_1,2P_2\right\}$
$=\{1,3,2\}$