Provide an appropriate response.
-True or false? The statement $\sin ^ { - 1 } ( \sin x ) = x$ for all real numbers in the interval $0 \leq x \leq \pi$.

Question

Quizplus · Accepted Answer

The statement is true because the sine function is bijective (both injective and surjective) in the interval $0 \leq x \leq \pi$, meaning each value of $x$ in this interval corresponds to a unique sine value, and every value in the range of the sine function corresponds to exactly one value in this interval. Therefore, $\sin^{-1}(\sin x) = x$ for all $x$ in the interval $0 \leq x \leq \pi$.

Provide an Appropriate Response sin⁡−1(sin⁡x)=x\sin ^ { - 1 } ( \sin x ) = xsin−1(sinx)=x

Provide an Appropriate Response $\sin ^ { - 1 } ( \sin x ) = x$