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Important Formulas: Sets, Relations & Functions
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FAQs on Important Formulas: Sets, Relations & Functions
| 1. What's the difference between a relation and a function in sets? |  |
Ans. A relation is any connection between elements of two sets, while a function is a special relation where each input has exactly one output. In a function, no two ordered pairs share the same first element with different second elements. Relations are broader; functions follow stricter mapping rules essential for JEE problem-solving.
| 2. How do I identify the domain and range of a function quickly? | |
Ans. Domain comprises all possible input values (x-values) a function accepts, while range includes all actual output values (y-values) produced. To find domain, identify restrictions like denominators ≠ 0 or expressions under square roots ≥ 0. Range requires analysing the function's behaviour across its domain, critical for solving JEE Main function problems efficiently.
| 3. What are the main types of functions I need to memorise for JEE? | |
Ans. Key function types include one-to-one (injective), onto (surjective), bijective, even, odd, inverse, composite, and periodic functions. One-to-one functions map distinct inputs to distinct outputs; onto functions cover the entire codomain. Understanding these classifications and their properties-including how to test even/odd functions using f(-x)-forms the foundation for advanced JEE questions.
| 4. Why do I keep getting confused between sets notation symbols? | |
Ans. Essential set symbols include ∪ (union-combines all elements), ∩ (intersection-common elements only), ⊂ (subset-all elements of A are in B), and ∖ (complement-elements not in the set). Union and intersection formulas like n(A∪B) = n(A) + n(B) - n(A∩B) frequently appear in JEE exams, so mastering notation prevents calculation errors.
| 5. How do inverse functions and composite functions connect in JEE problems? | |
Ans. Composite functions combine two functions: (f∘g)(x) = f(g(x)). Inverse functions reverse this operation: if f(a) = b, then f⁻¹(b) = a. The relationship f(f⁻¹(x)) = x always holds. JEE tests both composition techniques and inverse properties together, requiring clarity on how these operations interact within function chains.
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