The range of the function f(x) = ^ 7 - x 1pt P_ x - 3 is - Vidyadip

MCQ

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
$\{1, 2, 3, 4\}$
✓
$\{1, 2, 3\}$

✓

Answer

Correct option: D.

$\{1, 2, 3\}$

d
(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\}$.

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