Question

Range of the function $f(x)={ }^{7-x} P_{x-3}$, is

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

Answer 1

Answer: (B)

(As $f(x)={ }^{7-x} P_{x-3}$ is defined only for positive integer values of $x$ satisfying
$7-x > 0, x-3 > 0$ and $x-3 < 7-x$ or $x=3,4,5$
Range $(f)=\{f(3), f(4), f(5)\}$
$=\left\{{ }^{4} P_{0},{ }^{3} P_{1},{ }^{2} P_{2}\right\}=\{ 1 , 2,3\}$