Question:
The domain of the function $f(x) = 2\sin^{-1}(2x-1) - \dfrac{\pi}{4}$ is:
The domain of the function $f(x) = 2\sin^{-1}(2x-1) - \dfrac{\pi}{4}$ is:
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Always ensure argument of inverse trig functions lies within valid range.
Updated On: Apr 24, 2026
- $[-1,1]$
- $[0,1]$
- $[0,2]$
- $[2,5]$
- $[-2,2]$
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The Correct Option is B
Solution and Explanation
Concept:
• Domain of $\sin^{-1}(x)$ is $[-1,1]$
Step 1: Apply domain condition
\[ -1 \leq 2x - 1 \leq 1 \]
Step 2: Solve inequality
\[ -1 \leq 2x - 1 \leq 1 \] Add 1: \[ 0 \leq 2x \leq 2 \] Divide by 2: \[ 0 \leq x \leq 1 \] Final Conclusion:
\[ [0,1] \]
• Domain of $\sin^{-1}(x)$ is $[-1,1]$
Step 1: Apply domain condition
\[ -1 \leq 2x - 1 \leq 1 \]
Step 2: Solve inequality
\[ -1 \leq 2x - 1 \leq 1 \] Add 1: \[ 0 \leq 2x \leq 2 \] Divide by 2: \[ 0 \leq x \leq 1 \] Final Conclusion:
\[ [0,1] \]
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