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

Answer: (A)

$f\left(x\right)={}^{7-x}{P}_{x-3}$
$7-x\ge 0\Rightarrow x\le 7$
$x-3\ge 0\Rightarrow x\ge 3,$
and $7-x\ge x-3\Rightarrow x\le 5$
$\Rightarrow 3\le x\le 5\Rightarrow x=3,4,5\Rightarrow$ Range is $1,2,3.$