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RS Aggarwal - Mathematics

2. Functions

1. Relation
2. Functions
3. Binary Operations
4. Inverse Trigonometric Functions
5. Matrices
6. Determinants
7. Adjoint and Inverse of a Matrix
8. System of Linear Equations
9. Continuity and Differentiability
10. Differentiation
11. Applications of Derivatives
12. Indefinite Integral
13. Method of Integration
14. Some Special Integrals
15. Integration Using Partial Fractions
16. Definite Integrals
17. Area of Bounded Regions
18. Differential Equations and Their Formation
19. Differential Equations with Variable Separable
20. Homogeneous Differential Equations
21. Linear Differential Equations
22. Vectors and Their Properties
23. Scalar, or Dot, Product of Vectors
24. Cross, or Vector, Product of Vectors
25. Product of Three Vectors
26. Fundamental Concepts of 3-Dimensional Geometry
27. Straight Line in Space
28. The Plane
29. Probability
30. Bayes’s Theorem and its Applications
31. Probability Distribution
32. Binomial Distribution
33. Linear Programming

Exercise 2A

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Exercise 2B

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Exercise 2C

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Exercise 2D

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Objective Questions

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Q. 25.0( 1 Vote )

Prove that the fu

Class 12th RS Aggarwal - Mathematics 2. Functions

Answer :

To prove: function is one-one and into

Given: f: N → N : f(x)= 3x

We have,

f(x) = 3x

For, f(x₁) = f(x₂)

⇒ 3x₁ = 3x₂

⇒ x₁ = x₂

When, f(x₁) = f(x₂) then x₁ = x₂

∴ f(x) is one-one

f(x) = 3x

Let f(x) = y such that

⇒ y = 3x

If y = 1,

But as per question , hence x can not be

Hence f(x) is into

Hence Proved

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