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

{1, 2, 3, 4, 5}

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

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{1, 2, 3, 4}

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{1, 2, 3}

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Solution

The correct option is C ${1, 2, 3}$
$7 - x > 0, x - 3 \geq 0 a n d 7 - x \geq x - 3$
$\Rightarrow x < 7, x \geq 3 a n d x \leq 5$
Domain of the function f(x) is ${3, 4, 5}$
So, The range of the function is ${^{4} P_{0},^{3} P_{1},^{2} P_{2}} = {1, 2, 3}$

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