Class 12 Relations And Functions · Long Answer3 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Long Answer #177
Is f:R→R, f(x)=|x|, one-one or onto? Justify.
✅ Step-by-Step Solution
Final Answer: Neither one-one nor onto.
- Injectivity requires distinct inputs to have distinct images; surjectivity requires the entire real codomain.
- The distinct inputs 1 and −1 have the same image 1, so f is not injective.
- All outputs are nonnegative; −1 has no preimage, so f is not onto R.
- Hence f is neither one-one nor onto.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Injectivity requires distinct inputs to have distinct images; surjectivity requires the entire real codomain.
- [1 mark] The distinct inputs 1 and −1 have the same image 1, so f is not injective.
- [1 mark] All outputs are nonnegative; −1 has no preimage, so f is not onto R.
- [0.5 marks] Hence f is neither one-one nor onto.
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