Mark (√) against the correct answer in the following:
If $f(x)=x^{2}, g(x)=\tan x$ and $h(x)=\log x$ then $\{h \circ(g \circ f)\}\left(\sqrt{\frac{\pi}{4}}\right)=?$
A. 0
B. 1
C. $\frac{1}{\mathrm{x}}$
D. $\frac{1}{2} \log \frac{\pi}{4}$
$f(x)=x^{2}, g(x)=\tan x$ and $h(x)=\log x$
$\Rightarrow \mathrm{g}(\mathrm{f}(\mathrm{x}))=\tan (\mathrm{f}(\mathrm{x}))=\tan \left(\mathrm{x}^{2}\right)$
$\Rightarrow \mathrm{h}(\mathrm{g}(\mathrm{f}(\mathrm{x})))=\log (\mathrm{g}(\mathrm{f}(\mathrm{x})))=\log \left(\tan \left(\mathrm{x}^{2}\right)\right)$
$\Rightarrow \mathrm{h}\left(\mathrm{g}\left(\mathrm{f}\left(\sqrt{\frac{\pi}{4}}\right)\right)\right)=\log \left(\tan \left(\sqrt{\frac{\pi^{2}}{4}}\right)\right)=\log \left(\tan \left(\frac{\pi}{4}\right)\right)=\log (1)=0$
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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,