Class 12 Relations And Functions · Short Answer2 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Short Answer #168
Find the domain and range of f(x)=|x−1|/(x−1).
✅ Step-by-Step Solution
Final Answer: Domain R ∖ {1}; range {−1,1}.
- The denominator is zero at x=1, which must be excluded.
- For x>1 the quotient is 1; for x<1 it is −1, and both intervals are nonempty.
- Therefore the domain is R ∖ {1} and the range is {−1,1}.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The denominator is zero at x=1, which must be excluded.
- [1 mark] For x>1 the quotient is 1; for x<1 it is −1, and both intervals are nonempty.
- [0.5 marks] Therefore the domain is R ∖ {1} and the range is {−1,1}.
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