The range of the function f(x) = {}^{7 - x}P_ | vedclass

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(D) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r \in \mathbb{Z}^+ \cup \{0\}$.Here,$n = 7 - x$ and $r = x -

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$\{1, 2, 3\}$

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(D) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r \in \mathbb{Z}^+ \cup \{0\}$.Here,$n = 7 - x$ and $r = x - 3$.$1$. $n \ge r \implies 7 - x \ge x - 3 \implies 10 \ge 2x \implies x \le 5$.$2$. $r \ge 0 \implies x - 3 \ge 0 \implies x \ge 3$.$3$. $n \ge 0 \implies 7 - x \ge 0 \implies x \le 7$.Combining these,the domain is $x \in \{3, 4, 5\}$.Now,calculate $f(x)$ for each value in the domain:For $x = 3$: $f(3) = {}^{7-3}P_{3-3} = {}^{4}P_{0} = 1$.For $x = 4$: $f(4) = {}^{7-4}P_{4-3} = {}^{3}P_{1} = 3$.For $x = 5$: $f(5) = {}^{7-5}P_{5-3} = {}^{2}P_{2} = 2$.The range is the set of values ${f(3), f(4), f(5)} = \{1, 3, 2\}$,which is $\{1, 2, 3\}$.

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

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