Example 10 - 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
Example 10 Show that the function f : N → N, given by f (1) = f (2) = 1 and f (x) = x – 1, for every x > 2, is onto but not one-one. Here, f(x) = {█( 1 for 𝑥=1@ 1 for 𝑥=2@𝑥−1 for 𝑥>2)┤ Here, f (1) = 1 f (2) = 1 Check onto f: N → N f(x) = {█( 1 for 𝑥=1@ 1 for 𝑥=2@𝑥−1 for 𝑥>2)┤ Let f(x) = y , such that y ∈ N Here, y is a natural number & for every y, there is a value of x which is a natural number Hence f is onto
