Q.Using the graph of $y=\sin^{-1}x$, state whether the function is increasing or decreasing, and find its value at $x=0$.

The graph of $y=\sin^{-1}x$ is strictly increasing throughout its domain $[-1,1]$, since $\sin x$ is strictly increasing on the principal branch $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$, and reflecting an increasing curve in $y=x$ preserves that monotonic order. At $x=0$: $\sin^{-1}(0)=0$, sinc …

Reflecting an increasing function in $y=x$ keeps it increasing; read the value at $x=0$ directl …

Assuming that because $\sin x$ itself is not monotonic globally, $\sin^{-1}x$ must be decreasing somewhere -- but $\sin^{-1}x$ is built entirely from the strictly …