Question

The domain of the function $ \sin^{-1} x $ is

• A. \( [-\pi, \pi] \)
• B. \( [-1, 1] \)
• C. \( \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \)
• D. \( [0, 2\pi] \)

Hint:

The domain of inverse trigonometric functions is important for determining valid inputs. For \( \sin^{-1} x \), the input must lie between \( -1 \) and \( 1 \).

Answer 1

The Correct Option is B

We are given the function \( \sin^{-1} x \), which is the inverse sine function.
Step 1: Understanding the domain of \( \sin^{-1} x \)
The inverse sine function, \( \sin^{-1} x \), is defined for values of \( x \) between \( -1 \) and \( 1 \), inclusive.
This is because the sine function has a range of \( [-1, 1] \).
Step 2: Conclusion
Thus, the domain of the function \( \sin^{-1} x \) is \( [-1, 1] \), which corresponds to option (b).