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}
• C. {1, 2, 3, 4, 5}
• D. {1, 2, 3, 4, 5, 6}

Answer 1

The correct option is A {1, 2, 3}

${}^{7-x}{P}_{x-3}$ is defined for $x$ if
x-3 $\ge$ 0 and $7-x$ $\ge$ x-3 $=$ x $\le$ 5
The domain is $3,4,5$
$f\left(3\right)$ $=$ ${}^4{P}_0$ $=1$,
$f\left(4\right)$ $=$ ${}^3{P}_1$ $=3$,
$f\left(5\right)$ $=$ ${}^2{P}_2$ $=2$,
The range is $1,2,3$