Inverse Functions
Easymathematics
The range of cos⁻¹(x) is
Select the correct option:
Solution
Incorrect! Answer:
[0, π]
- Principal Branch Selection: For cosine, we restrict the range to an interval where it captures all values from -1 to 1 exactly once.
- Specific Interval: Since cos0=1 and cosπ=−1, we choose [0,π].
- Domain: The corresponding input domain is [−1,1].
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About This Question
- Subject
- mathematics
- Chapter
- trigonometry
- Topic
- inverse functions
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
[0, π]
- Principal Branch Selection: For cosine, we restrict the range to an interval where it captures all values from -1 to 1 exactly once.
- Specific Interval: Since cos0=1 and cosπ=−1, we choose [0,π].
- Domain: The corresponding input domain is [−1,1].
This easy difficulty mathematics question is from the chapter trigonometry, covering the topic of inverse functions. It appeared in the 2025 exam.
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