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, $7 - x > 0 \Rightarrow x < 7$
(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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