Set, Relation And Function 2

00:00:00 - Introduction and Welcome 00:00:09 - Finding the Range of a Quadratic Function: $f(x) = x^2 - 4x + 5$ 00:05:20 - Alternative Method: Using Derivatives for Minima/Maxima 00:06:18 - Determining the Domain of a Rational Function: $f(x) = \frac{\sqrt{x-1}}{x-4}$ 00:07:53 - Cartesian Product and Function Verification: $x^2 + y^2 = 1$ 00:12:54 - Solving Logarithmic Expressions: $\log_9 27 + \log_8 32$ 00:15:00 - Set Theory Problem: Students Playing Cricket, Football, and Tennis 00:18:13 - Identifying Rational Expressions among Algebraic Functions 00:20:19 - Verifying Set Identities using Venn Diagrams (Distributive & De Morgan’s Laws) 00:24:51 - Nested Square Root Simplification: $\sqrt{7\sqrt{7\sqrt{7}}}$ 00:28:48 - Finding the Inverse of a Linear Fractional Function 00:31:53 - Domain of Square Root Product Functions: $\sqrt{(2-x)(x-3)}$ 00:33:40 - Properties of Exponential Functions and Power Rules 00:35:18 - Circle Geometry Application: Ratio of Perimeter to Area 00:36:14 - Constraints on Logarithmic Bases and Domains 00:36:45 - Identifying Odd and Even Functions: $f(x) = \ln(\sqrt{x^2+1} + x)$ 00:39:51 - Solving Complex Set Intersection Problems (Indoor Games) 00:45:19 - Power Sets and Cardinality of Sets 00:47:11 - Analyzing Relations: Reflexive, Symmetric, and Transitive Properties 01:03:21 - Composite Functions: $g(f(x))$ and Polynomial Degrees 01:06:33 - Differentiation of Combined Functions: $h(x) = 5f(x) - xg(x)$ 01:07:44 - Periodicity of Trigonometric Functions: $\sin(x/4)$ and $\cos(4x/5)$ 01:14:35 - Finding the LCM Period for a Sum of Functions