Inverse Functions
Easymathematics
The range of sin⁻¹(x) is
Select the correct option:
Solution
Incorrect! Answer:
[-π/2, π/2]
- Bijectivity Constraint: Sine is periodic, so its inverse is only a function if we restrict the 'Range'.
- Principal Branch: By convention, we select the interval passing through 0 where the function is strictly increasing.
- Specific Interval: [−π/2,π/2].
- Domain Note: 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:
[-π/2, π/2]
- Bijectivity Constraint: Sine is periodic, so its inverse is only a function if we restrict the 'Range'.
- Principal Branch: By convention, we select the interval passing through 0 where the function is strictly increasing.
- Specific Interval: [−π/2,π/2].
- Domain Note: 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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