Question:
Mark (√) against the correct answer in the following:
If $f(x)=\frac{1}{(1-x)}$ then (f of of) $(x)=?$
A. $\frac{1}{(1-3 x)}$
B. $\frac{x}{(1+3 x)}$
C. $\mathrm{X}$
D. None of these
Solution:
$f(x)=\frac{1}{1-x}$
$\Rightarrow(f \circ f \circ f)(x)=f(f(f(x)))$
$\Rightarrow \mathrm{f}(\mathrm{f}(\mathrm{x}))=\frac{1}{1-\mathrm{f}(\mathrm{x})}=\frac{1}{1-\frac{1}{1-\mathrm{x}}}=\frac{1-\mathrm{x}}{1-\mathrm{x}-1}=\frac{\mathrm{x}-1}{\mathrm{x}}=1-\frac{1}{\mathrm{x}}$
$\Rightarrow \mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{x})))=\frac{1}{1-\mathrm{f}(\mathrm{f}(\mathrm{x}))}=\frac{1}{1-\left(1-\frac{1}{\mathrm{x}}\right)}=\frac{1}{\frac{1}{\mathrm{x}}}=\mathrm{x}$
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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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