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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
The domain of the function $\text{f}(\text{x})= ^{7-\text{x}}\text{P}_\text{x-3}$ is:
  • A
    $\{1, 2, 3\}$
  • B
    $\{3, 4, 5, 6\}$
  • ✓
    $\{3, 4, 5\}$
  • D
    $\{1, 2, 3, 4, 5\}$
✓

Answer

Correct option: C.
$\{3, 4, 5\}$
The function $\text{f}(\text{x})= ^{7-\text{x}}\text{P}_\text{x-3}$ is defined only if $x$ is an integer satisfying the following inequalities:
$7 - \text{x} ≥ 0.....(1)$
$\text{x} - 3 ≥ 0......(2)$
$7 - \text{x} ≥ \text{x} - 3........(3)$
Now, from $1,$ we get $\text{x} ≤ 7 ……… (4)$
from $2,$ we get $\text{x} ≥ 3 ……………. (5)$
and from $2,$ we get $\text{x} ≤ 5 ………. (6)$
From $4, 5$ and $6$, we get
$3 ≤ \text{x} ≤ 5$
So, the domain is $\{3, 4, 5\}.$

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