Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a function defined as :
$f(x)=\left\{\begin{array}{ccc}5, & \text { if } & x \leq 1 \\ a+b x, & \text { if } & 1 Then, $\mathrm{f}$ is :
continuous if $a=5$ and $b=5$
continuous if $a=-5$ and $b=10$
continuous if $a=0$ and $b=5$
not continuous for any values of $a$ and $b$
Correct Option: , 4
$f(x)=\left\{\begin{array}{ccc}5 & \text { if } & x \leq 1 \\ a+b x & \text { if } & 1 $f(1)=5, \quad f\left(1^{-}\right)=5, \quad f\left(1^{+}\right)=a+b$ $\mathrm{f}\left(3^{-}\right)=\mathrm{a}+3 \mathrm{~b}, \mathrm{f}(3)=\mathrm{b}+15, \mathrm{f}\left(3^{+}\right)=\mathrm{b}+15$ $\mathrm{f}\left(5^{-}\right)=\mathrm{b}+25 ; \mathrm{f}(5)=30 \quad \mathrm{f}\left(5^{+}\right)=30$ from above we concluded that $f$ is not continuous for any values of $a$ and $b$.
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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,