Let $f: R \rightarrow R: f(x)=(2 x+1)$ and $g: R \rightarrow R: g(x)=\left(x^{2}-2\right)$
Write down the formulae for
(i) (g o f)
(ii) (f o g)
(iii) (f o f)
(iv) (g o g)
(i) g o f
To find: g o f
Formula used: g o f = g(f(x))
Given: (i) f : R → R : f(x) = (2x + 1)
(ii) $g: R \rightarrow R: g(x)=\left(x^{2}-2\right)$
Solution: We have,
$g \circ f=g(f(x))=g(2 x+1)=\left[(2 x+1)^{2}-2\right]$
$\Rightarrow 4 x^{2}+4 x+1-2$
$\Rightarrow 4 x^{2}+4 x-1$
Ans). $g \circ f(x)=4 x^{2}+4 x-1$
(ii) f o g
To find: f o g
Formula used: f o g = f(g(x))
Given: (i) f : R → R : f(x) = (2x + 1)
(ii) $g: R \rightarrow R: g(x)=\left(x^{2}-2\right)$
Solution: We have,
$f \circ g=f(g(x))=f\left(x^{2}-2\right)=\left[2\left(x^{2}-2\right)+1\right]$
$\Rightarrow 2 x^{2}-4+1$
$\Rightarrow 2 x^{2}-3$
Ans). $f \circ g(x)=2 x^{2}-3$
(iii) $f$ o $f$
To find: f o f
Formula used: f o f = f(f(x))
Given: (i) f : R → R : f(x) = (2x + 1)
Solution: We have,
$f \circ f=f(f(x))=f(2 x+1)=[2(2 x+1)+1]$
$\Rightarrow 4 x+2+1$
$\Rightarrow 4 x+3$
Ans). $f$ of $f(x)=4 x+3$
(iv) $\mathrm{g} \circ \mathrm{g}$
To find: g o g
Formula used: g o g = g(g(x))
Given: (i) $g: R \rightarrow R: g(x)=\left(x^{2}-2\right)$
Solution: We have,
$g \circ g=g(g(x))=g\left(x^{2}-2\right)=\left[\left(x^{2}-2\right)^{2}-2\right]$
$\Rightarrow x^{4}-4 x^{2}+4-2$
$\Rightarrow x^{4}-4 x^{2}+2$
Ans). $g \circ g(x)=x^{4}-4 x^{2}+2$
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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,