Inverse Trigonometric Functions · Class 12 · CBSE · Science Mathematics
For the function f(x) = cos⁻¹(2x − 1), which of the following gives its domain and range?
Practice question from Inverse Trigonometric Functions (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · MCQ · Q-93768B
For the function f(x) = cos⁻¹(2x − 1), which of the following gives its domain and range?
- A.Domain [0, 1] and range [0, π]Correct answer
- B.Domain [−1, 1] and range [0, π]
- C.Domain [0, 1] and range [−π/2, π/2]
- D.Domain ℝ and range [0, π]
Solution
For cos⁻¹(2x − 1) to be defined, −1 ≤ 2x − 1 ≤ 1, which gives 0 ≤ x ≤ 1. The principal range of cos⁻¹ is [0, π].
More from Inverse Trigonometric Functions
- Using the principal value of the inverse sine function, find sin⁻¹(−√3/2).
- Evaluate cos⁻¹(cos(7π/6)) using the principal value of cos⁻¹.
- Evaluate sin⁻¹(3/5) + sin⁻¹(4/5), and justify your answer using the principal-value ranges.
- Using the principal value of the inverse tangent function, find tan⁻¹(−√3).
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