Question:
The minimum value of $f(x)=a^{a^{x}}+a^{1-a^{x}}$, where $a, x \in R$ and $a>0$, is equal to:
(1) $\mathrm{a}+\frac{1}{\mathrm{a}}$
(2) $a+1$
(3) $2 \mathrm{a}$
(4) $2 \sqrt{a}$
Correct Option: , 4
Solution:
$\mathrm{AM} \geq \mathrm{GM}$
$\frac{\mathrm{a}^{\mathrm{ax}}+\frac{\mathrm{a}}{\mathrm{anx}}}{2} \geq\left(\mathrm{a}^{\mathrm{ax} \cdot} \frac{\mathrm{a}}{\mathrm{a}^{\mathrm{ax}}}\right)^{1 / 2} \Rightarrow \mathrm{a}^{\mathrm{ax}}+\mathrm{a}^{1-\mathrm{ax}} \geq 2 \sqrt{\mathrm{a}}$
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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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