Question

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

• A. $\{1,2,3\}$
• B. $\{1,2,3,4,5\}$
• C. $\{1,2,3,4\}$
• D. $\{1,2,3,4.5,6\}$

Answer 1

The correct option is A

$\{1,2,3\}$

$f\left(x\right)$ is defined when
$\Rightarrow x-3\ge 0\Rightarrow x\ge 3,x-3\le 7-x\Rightarrow 2x\le 10\Rightarrow 3\le x\le 5\Rightarrow x=3\text{or}4\text{or}5$
Range $=\left\{f\right(3),f(4),f(5\left)\right\}=\left\{{}^4{P}_0{,}^3{P}_1{,}^2{P}_2\right\}=\{1,3,2\}$