AP DSC School Assistant Math Model Test 1

Concept:The inverse sine function $\sin^{-1} x$ is defined only for input values $x$ in the interval $[-1, 1]$. If the argument lies outside this range, the inverse is not defined.Explanation:We need to check whether the expression $\sin^{-1}\left(2\sin\frac{\pi}{2}\right)$ is valid.First, evaluate $\sin\frac{\pi}{2} = 1$.Then the argument becomes $2 \times 1 = 2$.The condition for existence of $\sin^{-1}x$ is $-1 \le x \le 1$.Here $x = 2$, which does not satisfy $-1 \le 2 \le 1$.Therefore, the given expression is not defined, i.e., its value does not exist as a real number.Answer:Option D: Does not exist