🔥 DEFINITION OF FUNCTION AND TYPES OF FUNCTION | NDA EXAM | BY DHEERAJ SIR | MISSION SELECTION

🔥 DEFINITION OF FUNCTION AND TYPES OF FUNCTION | NDA EXAM | BY DHEERAJ SIR | MISSION SELECTION
The video provides a comprehensive explanation of the definition and types of functions, specifically tailored for the NDA exam (0:00).

Here's a summary of the key topics covered:

Importance of Functions for NDA Exam: The instructor emphasizes that understanding functions, trigonometry, and calculus is crucial for the NDA exam, as concepts from functions are heavily used in calculus (0:20-0:43).
Definition of a Function: A relation from set A to set B is considered a function if every element in set A has a unique image in set B (2:50-3:25). If an element has more than one image, or no image at all, it's not a function (3:29-3:49). Examples like y²=x (3:59) (not a function) and y=√x (5:26) (a function) are used to illustrate this concept.
Venn Diagram and Cartesian Form for Functions: The video explains how to identify functions using Venn diagrams (10:01) and also introduces how to check if a relation in Cartesian form is a function by looking for repeated x-values (21:18-22:41).
Domain, Codomain, and Range:
Domain: The set of all input values (Set A) (14:02-15:00).
Codomain: The set of all possible output values (Set B) (15:03-15:12).
Range: The set of actual output values (the images within Set B) (15:57-16:47). It's highlighted that the range is always a subset of the codomain (16:51-17:14).
The concept of identifying domain and range from a function in Cartesian form is also explained (19:00-19:42).
Types of Functions Based on Operation: The video categorizes seven types of functions based on mathematical operations (addition, subtraction, multiplication, division). The instructor shows how certain operational relationships between f(x), f(y), and f(x op y) (where 'op' is an operation) correspond to specific function types (34:01-44:11).
Logarithmic Function: f(x) * f(y) = f(x + y) or f(x) - f(y) = f(x / y) (35:19-35:50, 40:37-41:03).
Exponential Function: f(x + y) = f(x) * f(y) or f(x - y) = f(x) / f(y) (34:54-35:16, 41:09-41:29).
Polynomial Function (x^n type): f(x) * f(y) = f(x * y) or f(x) / f(y) = f(x / y) (35:57-36:18, 41:40-41:57).
Linear Function (kx type): f(x) + f(y) = f(x + y) (36:23-36:34, 42:04-42:16).
Constant Function (k type): f(x) + f(y) = f(x * y) (43:51-44:11).
Solving NDA Exam Questions: The video concludes with examples of how to identify the type of function from its operational definition and then use given conditions to find the function's parameters and solve related problems, including those from NDA 2024 and NDA 2022 exams (44:47-50:29).
In this video, we explain Definition of Function and Types of Function in a simple & exam-oriented way.
This topic is very important for NDA exams.
👉 Video mein aap sikhenge:
✔ What is a Function? (Function ki definition)
✔ Domain, Codomain & Range (clear explanation)
✔ Types of Functions

📌 Concepts ko examples + easy language mein samjhaya gaya hai, taaki aap exam mein question easily solve kar sakein.
🎯 This video is specially designed for beginners & NDA aspirants.
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