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

MCQ

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

$\{1, 2, 3\}$

We know that
$7-\text{x}>0;\ \text{x}-3\geq0$ and $7-\text{x}\geq\text{x}-3$
$\Rightarrow\ \text{x}<7;\ \text{x}\geq3$ and $2\text{x}\leq10$
$\Rightarrow\ \text{x}<7;\ \text{x}\geq3$ and $\text{x}\leq5$
Therefore, $x = 3, 4, 5$
Range of $\text{f}=\Big\{^{(7-3)}\text{P}_{(3-3)},\ ^{(7-4)}\text{P}_{(4-3)},\ ^{(5-3)}\text{P}_{(7-5)}\Big\}$
$= \{4P_0, 3P_1, 2P_2\}$
$= \{1, 3, 2\}$
$= \{1, 2, 3\}$

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