Question

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

The correct option is A $\{1,2,3,4,5\}$

$f\left(x\right)=(7-x)!/(7-x-(x-3\left)\right)!=(7-x)!/(10–2x)!$

since permutation is defined only for natural numbers

thus,

now, from definition of nPr,n>=r

$7-x>=3-x$

$x<=5$

therefore, domain$=4,5$

$x=4$

$f\left(x\right)=3!/2!=3$

$x=5$

$f\left(x\right)=2!/0!=2$

$=>rangeoff=3,2$