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Welcome to this complete lecture on Unit 4 (Functions and Graphs) - Exercise 4.1 of 10th class math. In this video, we cover everything from basic conceptual definitions to step-by-step textbook solutions. We start with a detailed breakdown of what a function is, including its domain, codomain, and range. You will learn how to identify different types of functions—such as One-to-One, Onto (Surjective), and Bijective functions—using both conceptual mapping and graphical tests like the Vertical Line Test and Horizontal Line Test. Finally, we walk through every single question in Exercise 4.1, including Composite Functions and Inverse Functions. 📌 Timestamps: 00:00 - Introduction to Functions domain and codomain 10:15 - Difference between Codomain & Range 14:40 - Operations on functions 16:00 - Composition of functions 18:19 - What is an Inverse Function? 19:56 - Types of functions 22:34 - Vertical and horizontal line test 26:34 - Exercise 4.1 Q1 Solution (Function Algebra) 28:11 - Exercise 4.1 Q2 31:16 - Exercise 4.1 Q3 Solution (Composite Functions) 42:00 - Exercise 4.1 Q4 Find value of k 44:33 - Exercise 4.1 Q5 Solution (Evaluating Functions) 47:51 - Exercise 4.1 Q6 Solution (Finding Inverse) 53:43 - Exercise 4.1 Q7 Inverse Functions 56:39 - Exercise 4.1 Q8 Solution (Verification of Inverses) 1:07:51 - Exercise 4.1 Q9 Solution (Domain & Range of Inverses) 1:20:40 - Exercise 4.1 Q10 Find a If this video helped you clear your concepts, make sure to like, comment with any questions, and subscribe for more 10th Class Math lecture series!

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