Question:
The domain of the function $f(x)=\sqrt{5|x|-x^{2}-6}$ is
(a) (−3, − 2) ∪ (2, 3)
(b) [−3, − 2) ∪ [2, 3)
(c) [−3, − 2] ∪ [2, 3]
(d) None of these
Solution:
(c) [−3, − 2] ∪ [2, 3]
$f(x)=\sqrt{5|x|-x^{2}-6}$
For $f(x)$ to be defined, $5|x|-x^{2}-6 \geq 0$
$\Rightarrow 5|x|-x^{2}-6 \geq 0$
$\Rightarrow x^{2}-5|x|+6 \leq 0$For $x>0,|x|=x$
$\Rightarrow x^{2}-5 x+6 \leq 0$
$\Rightarrow(x-2)(x-3) \leq 0$
$\Rightarrow x \in[2,3] \quad \ldots \ldots \ldots(1)$
For $x<0,|x|=-x$
$\Rightarrow x^{2}+5 x+6 \leq 0$
$\Rightarrow(x+2)(x+3) \leq 0$
$\Rightarrow x \in[-3,-2] \quad \ldots \ldots(2)$
From (1) and (2),
$x \in[-3,-2] \cup[2,3]$
or, $\operatorname{dom}(f)=[-3,-2] \cup[2,3]$
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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