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Class 12MathematicsInverse Trigonometric FunctionsDomain and rangeMedium
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Under which condition is \(\sin(\sin^{-1}x)\) equal to \(x\)?

Answer and explanation

Correct answer: Only for (x\in[-1,1])

The domain of \(\sin^{-1}x\) is \([-1,1]\), so \(\sin(\sin^{-1}x)=x\) there. In composition, check the inner function domain.

Related tags

Inverse-Trigonometric-FunctionsCompositionDomainDomain And RangeInverse Trigonometric FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1What is the domain of \(\sec^{-1}x\) ?
  2. 2What is the domain of \(\cosec^{-1}x\) ?
  3. 3In the inverse trigonometric function \(\sin^{-1}x\), what is the domain of \(\sin^{-1}x\)?
  4. 4For the inverse trigonometric function \(\cos^{-1}x\), what is the domain of \(\cos^{-1}x\)?
  5. 5What is the domain of tan⁻¹x?
  6. 6Which statement is correct about \(\cos^{-1}\left(-2\right)\)?
  7. 7Which statement is correct for \(\sin^{-1}\left(\frac{7}{6}\right)\)?
  8. 8Which option is correct for \(\cos^{-1}\left(\frac{11}{10}\right)\)?
  9. 9Which statement is correct for \(\sec^{-1}\left(\frac{3}{2}\right)\)?
  10. 10Which statement is correct for \(cosec^{-1}\left(-\frac{5}{4}\right)\)?
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