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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
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
    $\{1,2,3,4,3,6\}$
  • 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 $\text{f}=\Big\{^{(7-3)}\text{P}_{(3-3)},\ ^{(7-4)}\text{P}_{(4-3)},\ ^{(5-3)}\text{P}_{(7-5)}\Big\}$
$=\left\{4 P_0, 3 P_1, 2 P_2\right\}$
$=\{1,3,2\}$
$=\{1,2,3\}$

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