Ex 1.2, 12 (MCQ) - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
To prove one-one & onto (injective, surjective, bijective)
One One function
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Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
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To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Ex 1.2, 12 Let f: R → R be defined as f(x) = 3x. Choose the correct answer. (A) f is one-one ,onto (B) f is many-one onto (C) f is one-one but not onto (D) f is neither one-one nor onto f(x) = 3x Checking one-one f (x1) = 3x1 f (x2) = 3x2 Putting f(x1) = f(x2) 3x1 = 3 x2 Rough One-one Steps: 1. Calculate f(x1) 2. Calculate f(x2) 3. Putting f(x1) = f(x2) we have to prove x1 = x2 x1 = x2 Hence, if f(x1) = f(x2) , x1 = x2 ∴ function f is one-one Onto f(x) = 3x Let f(x) = y , such that y ∈ R 3x = y x = 𝑦/3 Now, Checking for y = f(x) Putting value of x in f(x) f(x) = f(𝑦/3) = 3(y/3) = 𝑦 Thus, for every y ∈ R, there exists x ∈ R such that f(x) = y Hence, f is onto So, f is one-one and onto ∴ A is the correct option
