Range of function f(x){ = ^{7 - x}}{kern 1pt} {P_{x - 3}} is

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1.Relation and Function

hard

The range of the function $f(x){ = ^{7 - x}}{\kern 1pt} {P_{x - 3}}$ is

A

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

B

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

C

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

D

$\{1, 2, 3\}$

(AIEEE-2004)

Solution

(d) For $^{7 – x}{P_{x – 3}}$ to be defined, $7 – x > 0 \Rightarrow x < 7$

$x – 3 \ge 0 \Rightarrow x \ge 3$; $7 – x \ge x – 3 \Rightarrow x \le 5$

$\therefore$ $x \in \left\{ {3,\,4,\,5} \right\}$ ==> $f(3) = 1,\;f(4) = 3,\,\,f(5) = 2$

So, the range of function $ = \left\{ {1,\,\,2,\,\,3} \right\}$.

Standard 12

Mathematics

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