Let $A=\{1,2,3,4\} .$ Let $f: A \rightarrow A$ and $g: A \rightarrow A$,
defined by $f=\{(1,4),(2,1),(3,3),(4,2)\}$ and $g=\{(1,3),(2,1),(3,2),(4,4)\}$
Find (i) g of (ii) f o g (iii) f o f.
(i) $\mathrm{g}$ o $\mathrm{f}$
To find: $g$ o $f$
Formula used: $g$ o $f=g(f(x))$
Given: $f=\{(1,4),(2,1),(3,3),(4,2)\}$ and $g=\{(1,3),(2,1)$
$(3,2),(4,4)\}$
Solution: We have,
$g \circ f(1)=g(f(1))=g(4)=4$
$g \circ f(2)=g(f(2))=g(1)=3$
$g \circ f(3)=g(f(3))=g(3)=2$
$g \circ f(4)=g(f(4))=g(2)=1$
Ans) g of $f=\{(1,4),(2,3),(3,2),(4,1)\}$
(ii) $f \circ g$
To find: f o g
Formula used: f o g = f(g(x))
Given: f = {(1, 4), (2, 1), (3, 3), (4, 2)} and g = {(1, 3), (2, 1),
(3, 2), (4, 4)}
Solution: We have,
fog(1) = f(g(1)) = f(3) = 3
fog(2) = f(g(2)) = f(1) = 4
fog(3) = f(g(3)) = f(2) = 1
fog(4) = f(g(4)) = f(4) = 2
Ans) f o g = {(1, 3), (2, 4), (3, 1), (4, 2)}
(iii) f o f
To find: $f$ o $f$
Formula used: $f$ o $f=f(f(x))$
Given: $f=\{(1,4),(2,1),(3,3),(4,2)\}$
Solution: We have,
fof $(1)=f(f(1))=f(4)=2$
fof $(2)=f(f(2))=f(1)=4$
fof $(3)=f(f(3))=f(3)=3$
fof $(4)=f(f(4))=f(2)=1$
Ans) fo f $=\{(1,2),(2,4),(3,3),(4,1)\}$
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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,