Question

Domain of the function \( \sin^{-1}(2x - 1) \) is:

• A. \( [0, 1] \)
• B. \( [0, \infty) \)
• C. \( [-\infty, 1] \)
• D. \( [1, \infty) \)
• E. \( [-1, 1] \)

Hint:

For inverse sine functions, always ensure the argument lies within the valid range of -1 to 1.

Answer 1

The Correct Option is A

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 \( [0, 1] \).