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 \ge0,x-3 \ge0 $ and $ 7-x \ge x-3 $
$ \Rightarrow 3 \le x \le5 $ 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\}$