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)

$f\left(x\right) = \,{}^{7-x}P_{x-3}$
$7 − x \ge 0 \quad⇒ \quad x \le 7$
$x − 3 \ge 0 \quad ⇒\quad x \ge 3 ,$
and $7 − x \ge x − 3 \quad ⇒ \quad x \le 5$
$⇒ 3 \le x \le 5⇒ x = 3, 4, 5 ⇒$ Range is $1, 2, 3.$