Скачать или смотреть Exercise 2(d) Relations and Functions | Domain, Range& Function Checking | Inter 1st Year & Class 11

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This video covers *Exercise 2(d)* from *Chapter 2 – Relations and Functions* of *Intermediate 1st Year Mathematics* and also aligns with **CBSE Class 11 Maths syllabus**.

In this video, we learn how to:
✔️ Apply function difference formula
✔️ Find domain and range of rational, square root and modulus functions
✔️ Understand how to evaluate domain exclusions in rational functions
✔️ Check whether a given relation is a function or not
✔️ Test properties of functions through logic and counterexamples
✔️ Solve real examples using highest prime factor function

🎯 Concepts Explained:
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🔹 Function difference:
  \( \frac{f(1.1) - f(1)}{1.1 - 1} \) where \( f(x) = x^2 \)

🔹 Rational Function Domain:
  Find domain of \( f(x) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12} \)

🔹 Square Root Function Domain & Range:
  \( f(x) = \sqrt{x - 1} \)

🔹 Modulus Function Domain & Range:
  \( f(x) = |x - 1| \)

🔹 Composite Rational Function Range:
  \( f(x) = \frac{x^2}{1 + x^2} \)

🔹 Properties of relation on N:
  Check if \( R = \{(a, b): a = b^2\} \) satisfies:
   (i) ∈ R ∀ a
   (ii) ∈ R implies (b, a) ∈ R
   (iii) ∈ R implies (a, c) ∈ R

🔹 Whether f is a function from A to B:
  Check relation between sets A and B
  Ex: If multiple ordered pairs have the same first element – not a function

🔹 Function from Z to Z:
  If \( f = \{(ab, a + b)\} \) is a function or not

🔹 Function using Highest Prime Factor:
  \( f(n) = \text{highest prime factor of } n \)

🧠 Key Ideas:
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• Domain exclusions from denominators
• Function logic using set theory
• Identifying multiple outputs for same input
• Composite function transformation

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▶️ Watch Previous Exercises from Chapter 2:
👉    • Intermediate Mathmatics 1st Year  - Relati...  

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