Class 12 Relations And Functions · Short Answer2 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Short Answer #169
Find the range of f(x)=1/(2−cos x), x∈R.
✅ Step-by-Step Solution
Final Answer: [1/3,1]
- Since −1≤cos x≤1, the denominator lies in [1,3] and is positive.
- Taking reciprocals gives 1/3≤f(x)≤1; continuity of cosine supplies every denominator between 1 and 3.
- The range is [1/3,1], with endpoints attained when cos x=−1 and 1 respectively.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Since −1≤cos x≤1, the denominator lies in [1,3] and is positive.
- [1 mark] Taking reciprocals gives 1/3≤f(x)≤1; continuity of cosine supplies every denominator between 1 and 3.
- [0.5 marks] The range is [1/3,1], with endpoints attained when cos x=−1 and 1 respectively.
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