The domain of the function f(x) = {}^{(10-x)} | vedclass

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(D) For the combination ${}^{n}C_{r}$ to be defined, $n$ and $r$ must be non-negative integers such that $n \ge r \ge 0$.$1$. $n \ge 0 \implies 10 - x

Vedclass · Accepted Answer

$\{6, 7, 8\}$

Vedclass · Answer

(D) For the combination ${}^{n}C_{r}$ to be defined, $n$ and $r$ must be non-negative integers such that $n \ge r \ge 0$.$1$. $n \ge 0 \implies 10 - x \ge 0 \implies x \le 10$.$2$. $r \ge 0 \implies x - 6 \ge 0 \implies x \ge 6$.$3$. $n \ge r \implies 10 - x \ge x - 6 \implies 16 \ge 2x \implies x \le 8$.Combining these conditions: $6 \le x \le 8$ and $x$ must be an integer.Thus, $x \in \{6, 7, 8\}$.Therefore, the correct option is $D$.

The domain of the function $f(x) = {}^{(10-x)}C_{(x-6)}$ is...

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