Class 12 Relations And Functions · Short Answer2 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Short Answer #207
Prove f:R→R, f(x)=3x, is bijective.
✅ Step-by-Step Solution
Final Answer: Bijective.
- If f(u)=f(v), then 3u=3v.
- Thus u=v, proving injectivity. For every y∈R choose x=y/3, giving f(x)=y and proving onto.
- Hence f is bijective, with inverse y↦y/3.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] If f(u)=f(v), then 3u=3v.
- [1 mark] Thus u=v, proving injectivity. For every y∈R choose x=y/3, giving f(x)=y and proving onto.
- [0.5 marks] Hence f is bijective, with inverse y↦y/3.
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