Question:
Let $f$ and $g$ be two functions from $R$ into $R$, defined by $f(x)=|x|+x$ and $g(x)=|x|-x$ for all $x \in R .$ Find $f \circ g$ and $g \circ f$.
Solution:
To Find: Inverse of f o g and g o f
Given: $f(x)=|x|+x$ and $g(x)=|x|-x$ for all $x \in R$
fog $(x)=f(g(x))=|g(x)|+g(x)=|| x|-x|+|x|-x$
Case 1$)$ when $x \geq 0$
$f(g(x))=0$ (i.e. $|x|-x)$
Case 2$)$ when $x<0$
$f(g(x))=-4 x$
$g \circ f(x)=g(f(x))=|f(x)|-f(x)=|| x|+x|-|x|-x$
Case 1 ) when $x \geq 0$
$g(f(x))=0($ i.e. $|x|-x)$
Case 2$)$ when $x<0$
$g(f(x))=0$
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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,
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