Question

The range of the function $f\left(x\right)=\,{}^{7-x}P_{x-3}$ is

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

Answer 1

Answer: (A)

The given function $f(x)={ }^{7-x} P_{x-3}$ would be defined, if
(i) $7-x>0$
$\Rightarrow x<7$
(ii) $x-3 \geq 0$
$\Rightarrow x \geq 3$
(iii) $(x-3) \leq(7-x)$
$\Rightarrow 2 x \leq 10$
$\Rightarrow x \leq 5$
$\Rightarrow x=3,4,5$
Hence, range of $f(x)=\left\{{ }^{4} P_{0},{ }^{3} P_{2},{ }^{2} P_{2}\right\}$
Range of $f(x)=\{1,3,2\}$