The range of the function f(x)=P x−3 7−x is

f(x)=7−xp x−3 is defined iff7−x≥x−3 and x−3≥0⇒ 7+3≥x+x,x≥3⇒ 2x≤10⇒ x≤5∴ 3≤x≤5∴ Range = {f(3), f(4), f(5)}= {p0 4, p1 3, p2 2}={1,3,2}

The range of the function f(x)=P x−3 7−x is

f(x)=7−xp x−3 is defined iff7−x≥x−3 and x−3≥0⇒ 7+3≥x+x,x≥3⇒ 2x≤10⇒ x≤5∴ 3≤x≤5∴ Range = {f(3), f(4), f(5)}= {p0 4, p1 3, p2 2}={1,3,2}

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$T h e r a n g e o f t h e f u n c t i o n f (x) = {}^{7 - x}P_{x - 3} i s$

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${1, 2, 3, 4}$

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

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

${1, 2, 3}$

answer is A.

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Detailed Solution

$\begin{array}{l} f (x) = 7 - x p_{x - 3} i s d e f i n e d i f f \\ 7 - x \geq x - 3 a n d x - 3 \geq 0 \\ \Rightarrow 7 + 3 \geq x + x, x \geq 3 \\ \Rightarrow 2 x \leq 10 \\ \Rightarrow x \leq 5 \\ ∴ 3 \leq x \leq 5 \\ ∴ R a n g e = {f (3), f (4), f (5)} \\ = {{}^{4}p_{0}, {}^{3}p_{1}, {}^{2}p_{2}} \\ = {1, 3, 2} \end{array}$