# The Domain of the Function F ( X ) = √ 5 | X | − X 2 − 6 Is(A) (−3, − 2) ∪ (2, 3) (B) [−3, − 2) ∪ [2, 3) (C) [−3, − 2] ∪ [2, 3] (D) None of These - Mathematics

MCQ

The domain of the function $f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}$ is

#### Options

• (a) (−3, − 2) ∪ (2, 3)

• (b) [−3, − 2) ∪ [2, 3)

• (c) [−3, − 2] ∪ [2, 3]

• (d) None of these

#### Solution

(c) [−3, − 2] ∪ [2, 3]

$f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}$

$\text{ For f(x) to be defined,} 5\left| x \right| - x^2 - 6 \geq 0$
$\Rightarrow 5\left| x \right| - x^2 - 6 \geq 0$
$\Rightarrow x {}^2 - 5\left| x \right| + 6 \leq 0$
$\text{ For } x > 0, \left| x \right| = x$
$\Rightarrow x {}^2 - 5x + 6 \leq 0$
$\Rightarrow (x - 2)(x - 3) \leq 0$
$\Rightarrow x \in [2, 3] . . . . . . . . (1)$
$\text{ [For } x < 0, \left| x \right| = - x$
$\Rightarrow x {}^2 + 5x + 6 \leq 0$
$\Rightarrow (x + 2)(x + 3) \leq 0$
$\Rightarrow x \in [ - 3, - 2] . . . . . . . (2)$
$\text{ From (1) and (2) } ,$
$x \in [ - 3, - 2] \cup [2, 3]$
$\text{ or, dom } (f) = [ - 3, - 2] \cup [2, 3]$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Q 39 | Page 45