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

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Question

(A) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r$ must be non-negative integers.Here,$n = 7-x$ and $r = x-1$

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$x \in \{1, 2, 3, 4\}$

Vedclass · Answer

(A) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r$ must be non-negative integers.Here,$n = 7-x$ and $r = x-1$.Condition $1$: $n \ge r \implies 7-x \ge x-1 \implies 8 \ge 2x \implies x \le 4$.Condition $2$: $r \ge 0 \implies x-1 \ge 0 \implies x \ge 1$.Condition $3$: $n \ge 0 \implies 7-x \ge 0 \implies x \le 7$.Combining these,we get $1 \le x \le 4$.Since $x$ must be an integer for the permutation notation,the domain is $\{1, 2, 3, 4\}$.

The domain of the function $f(x) = {}^{7-x}P_{x-1}$ is:

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