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Ex 1.3, 13 (MCQ) - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
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
- To prove one-one & onto (injective, surjective, bijective)
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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 1.3, 13 If f: R → R be given by f(x) = 〖"(3 – x3)" 〗^(1/3) , then fof(x) is (A) "x" ^(1/3) (B) x3 (C) x (D) (3 – x3) f(x) = 〖"(3 – x3)" 〗^(1/3) f(f(x)) = 〖"(3 – f(x)3)" 〗^(1/3) fof(x) = ("3 – " 〖"(3 – x3)" 〗^(𝟏/𝟑 × 𝟑) )^(1/3) = ("3 – " 〖"(3 – x3)" 〗^1 )^(1/3) = ("3 – 3 + x3" )^(1/3) = ("x3" )^(1/3) = x Hence fof(x) = x So, C is the correct answer
