Question:
Domain of the function \( \sin^{-1}(2x - 1) \) is:
Domain of the function \( \sin^{-1}(2x - 1) \) is:
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For inverse sine functions, always ensure the argument lies within the valid range of -1 to 1.
Updated On: Mar 7, 2025
- \( [0, 1] \)
- \( [0, \infty) \)
- \( [-\infty, 1] \)
- \( [1, \infty) \)
- \( [-1, 1] \)
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The Correct Option is A
Solution and Explanation
For \( \sin^{-1}(y) \) to be valid, \( y \) must lie between -1 and 1.
Therefore, the expression \( 2x - 1 \) must lie between -1 and 1: \[ -1 \leq 2x - 1 \leq 1 \] Solving this inequality: \[ 0 \leq x \leq 1 \] Thus, the domain is \( [0, 1] \).
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