Question:
Let $f: R \rightarrow R: f(x)=\left(3-x^{3}\right)^{1 / 3}$. Find $f$ o $f$.
Solution:
To find: $f$ of
Formula used: (i) $f$ o $f=f(f(x))$
Given: (i) $f: R \rightarrow R: f(x)=\left(3-x^{3}\right)^{1 / 3}$
We have,
$f \circ f=f(f(x))=f\left(\left(3-x^{3}\right)^{1 / 3}\right)$
$f \circ f=\left[3-\left\{\left(3-x^{3}\right)^{1 / 3}\right\}^{3}\right]^{1 / 3}$
$=\left[3-\left(3-x^{3}\right)\right]^{1 / 3}$
$=\left[3-3+x^{3}\right]^{1 / 3}$
$=\left[x^{3}\right]^{1 / 3}$
$=x$
Ans) $f$ o $f(x)=x$
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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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