Question:
Mark (√) against the correct answer in the following:
$f: N \rightarrow N: f(x)=2 x$ is
A. one - one and onto
B. one - one and into
C. many - one and onto
D. many - one and into
Solution:
$f(x)=2 x$
For One - One
$f\left(x_{1}\right)=2 x_{1}$
$f\left(x_{2}\right)=2 x_{2}$
put $f\left(x_{1}\right)=f\left(x_{2}\right)$ we get
$2 x_{1}=2 x_{2}$
Hence, if $f\left(x_{1}\right)=f\left(x_{2}\right), x_{1}=x_{2}$
Function $\mathrm{f}$ is one - one
For Onto
$f(x)=2 x$
let $f(x)=y$, such that $y \in N$
$2 x=y$
$\Rightarrow \mathrm{X}=\frac{\mathrm{y}}{2}$
If $y=1$
$x=\frac{1}{2}=0.5$
which is not possible as $x \in N$
Hence, $f$ is not onto., $f$ is into
Hence, option b is correct
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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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