Let $f: R \rightarrow R: f(x)=x^{2}+2$ and $g: R \rightarrow R: g(x)=\frac{x}{x-1}, x \neq 1$. find $f$ o $g$ and $g$ o $f$ and hence find (f o $g$ ) (2)
and (g o f) $(-3)$
To find: $f \circ g, g \circ f,(f \circ g)(2)$ and $(g \circ f)(-3)$
Formula used: (i) $f \circ g=f(g(x))$
(ii) $g \circ f=g(f(x))$
Given: (i) $f: R \rightarrow R: f(x)=x^{2}+2$
(ii) $g: R \rightarrow R: g(x)=\frac{x}{x-1}, x \neq 1$
f o g = f(g(x))
$\Rightarrow f\left(\frac{x}{x-1}\right)$
$\Rightarrow\left(\frac{x}{x-1}\right)^{2}+2$
Ans $) \Rightarrow \frac{(x)^{2}}{(x-1)^{2}}+2$
fog $(2)=\frac{(2)^{2}}{(2-1)^{2}}+2$
$=\frac{4}{1}+2$
Ans) = 6
g o f = g(f(x))
$\Rightarrow g\left(x^{2}+2\right)$
$\Rightarrow \frac{x^{2}+2}{x^{2}+2-1}$
Ans $) \Rightarrow \frac{x^{2}+2}{x^{2}+1}$
$(g \circ f)(-3)=\frac{-3^{2}+2}{-3^{2}+1}$
$=\frac{9+2}{9+1}$
Ans) $=\frac{11}{10}$
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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,