Question:
Let $f: Z \rightarrow Z: f(x)=2 x$. Find $g: Z \rightarrow Z: g \circ f=l_{Z}$.
Solution:
To find: $g: Z \rightarrow Z: g \circ f=I_{Z}$
Formula used: (i) $f \circ g=f(g(x))$
(ii) g o f = g(f(x))
Given: (i) $g: Z \rightarrow Z:$ g of $=I_{Z}$
Solution: We have,
$f(x)=2 x$
Let $f(x)=y$
⇒ y = 2x
$\Rightarrow \mathrm{x}=\frac{\mathrm{y}}{2}$
$\Rightarrow \mathrm{x}=\frac{\mathrm{y}}{2}$
Let $g(y)=\frac{y}{2}$
Where g: Z → Z
For g o f,
⇒ g(f(x))
⇒ g(2x)
$\Rightarrow \frac{2 x}{2}$
$\Rightarrow x=I_{Z}$
Clearly we can see that $(g \circ f)=x=l z$
The required function is $g(x)=\frac{x}{2}$
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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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