What is \(\sin(\sin^{-1}x)\) equal to when \(x\in[-1,1]\)?

Correct answer: \(x\)

By definition, \(\sin^{-1}x\) gives the angle \(y\in[-\pi/2,\pi/2]\) such that \(\sin y=x\). Applying sine to that angle returns the original value: \(\sin(\sin^{-1}x)=x\) for \(x\in[-1,1]\). Option B (\(\sin^{-1}x\)) is incorrect because it is the inverse value itself; composing in the given order returns \(x\), not the inverse. Exam tip: always check the domain of the inner function and the principal range of the inverse to verify such compositions quickly.