Q81.Let A = { x ∈R : x is not a positive integer} . Define a function f : A →R as f(x) = x−12x , then f is: (1) Injective but not surjective (2) Not injective (3) Surjective but not injective (4) Neither injective nor surjective
What This Question Tests
This question evaluates the understanding of injectivity and surjectivity of a function, requiring careful algebraic analysis and consideration of the function's restricted domain and codomain.
Concepts Tested
Formulas Used
f(x₁) = f(x₂) implies x₁ = x₂ for injectivity
For every y in codomain, there exists x in domain such that f(x)=y for surjectivity
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📋 Question Details
- Chapter
- Sets Relations Functions
- Topic
- Types of Functions (Injective, Surjective)
- Year
- 2019
- Shift
- 09 Jan Shift 2
- Q Number
- Q81
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 1: Relations and Functions
More from this Chapter
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