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

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${1, 2, 3, 4}$

${1, 2, 3, 4, 5, 6}$

${1, 2, 3}$

${1, 2, 3, 4, 5,}$

answer is C.

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Detailed Solution

$7 - x \geq 1, x - 3 \geq 0$

and $7 - x \geq x - 3$

$\Rightarrow x \leq 6, x \geq 3, x \leq 5$

Thus $3 \leq x \leq 5$

$∴$ Range $\begin{array}{l} = \{4 P_{0}, 3 P_{1}, 2 P_{2}\} \\ = {1, 3, 2} \end{array}$

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