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) $x-3\ge 0$
$\Rightarrow x\ge 3$
(iii) $(x-3)\le (7-x)$
$\Rightarrow 2x\le 10$
$\Rightarrow x\le 5$
$\Rightarrow x=3,4,5$
Hence, range of $f(x)=\left\{{}^4{P}_0,{}^3{P}_2,{}^2{P}_2\right\}$
Range of $f(x)=\{1,3,2\}$