Question:
Let $\mathrm{f}(\mathrm{x})=\log _{\mathrm{e}}(\sin \mathrm{x}),(0<\mathrm{x}<\pi)$ and $g(x)=\sin ^{-1}\left(e^{-x}\right),(x \geq 0)$. If $\alpha$ is a positive real number such that $\mathrm{a}=(\mathrm{fog})^{\prime}(\alpha)$ and $\mathrm{b}=(\mathrm{fog})(\alpha)$, then :
$a \alpha^{2}-b \alpha-a=0$
$a \alpha^{2}+b \alpha-a=-2 \alpha^{2}$
$a \alpha^{2}+b \alpha+a=0$
$a \alpha^{2}-b \alpha-a=1$
Correct Option: , 4
Solution:
fog $(x)=(-x) \Rightarrow(f g(\alpha))=-\alpha=b$
$(f g(x))^{\prime}=-1 \Rightarrow(f g(\alpha))^{\prime}=-1=a$
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All Study Material
- 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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