RELATIONS & FUNCTIONS
Resources & Insights
Explore relations and functions, fundamental concepts in mathematics that describe how elements from one set relate to elements in another. Learn about domain, range, types of functions, and their graphical representations. Perfect for students building a foundation in algebra, calculus, and advanced mathematical analysis.
Solving the Surjective Function Equation f(x) for Positive Real Numbers
Discover the surjective functions f(x) that satisfy the equation 2xf(f(x)) = f(x)(x + f(f(x))) for all positive real numbers x. READ MORE...
Solving Functional Equations: Finding f(x) and g(x)
Discover how to find functions f(x) and g(x) that satisfy a specific functional equation. Explore different cases and solutions. READ MORE...
Solving Surjective Functions: A Functional Equation Approach
Discover how to find all surjective functions f:R→R satisfying a specific functional equation. Learn the key steps and techniques. READ MORE...
Solving Functional Equations: Tips and Tricks for Midterm Prep
Struggling with functional equations for your math midterm? This post provides tips and tricks including substituting values using mathematical induction and finding fixed points to help you solve these challenging problems. READ MORE...
Understanding Vectors in Mathematics: Definition Operations and Applications
Learn about vectors in mathematics their properties and how they’re used in physics computer graphics and machine learning. READ MORE...
Proving Mathematical Propositions: Direct Indirect and Other Methods
Learn various methods for proving mathematical statements including direct proof indirect proof (contradiction and contrapositive) proof by cases and mathematical induction. Explore examples and applications. READ MORE...
Navigating the CBSE Board Exams 2025: A Comprehensive Guide
Conquer the CBSE Board Exams 2025 with our guide! Learn effective study strategies, time management tips, and overcome exam anxiety for success. READ MORE...
Cartesian Product
The cartesian product of two sets A and B is defined as a set formed by all the possible ordered pairs of elements from A and B, such that the first element comes from set A and the second element comes from set B. The cartesian product is denoted as A × B. Let a and b represent arbitrary elements from set A and set B respectively. So, a ∈ A and b ∈ B. Then A × B = { (a,b) | a ∈ A, b ∈ B }. Remember ☞ If A has m elements and B has n elements then their cartesian product will have m × n elements.If n(A) = m and n(B)=n , then n(A […] READ MORE...