Question

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

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

Answer 1

Answer: (D)

${}^{7-x}{P}_{x-3}$ is defined
if $7-x\ge 0,x-3\ge 0$ and $7-x\ge x-3$
$\Rightarrow 3\le x\le 5$ and $x\in I$
$\therefore x=3,4,5\therefore f\left(3\right){=}^{7-3}{P}_{3-3}{=}^4{P}_0=1$
$\therefore f\left(4\right){=}^{7-4}{P}_{4-3}{=}^3{P}_1=3$
$\therefore f\left(5\right){=}^{7-5}{P}_{5-3}{=}^2{P}_2=2$
$\therefore$ Range =$\left\{1,2,3\right\}$