The implied domain of y = Cos-1(sin3x)
Solution:
The < and > represent greater than equal to or less than equal to (i dont no what key to press to get them)
-1 < sin3x < 1
sin3x = 1
3x = pie/2
x = pie/6
Therefor [-pie/6, pie/6]
You know that the domain for $\displaystyle y = \cos^{-1} (x)$ is $\displaystyle [-1, 1]$.
As you noted, $\displaystyle \sin 3x \in [-1,1]$ for all x values. Since for every x, sin 3x will produce a number between -1 and 1 and $\displaystyle y=\cos^{-1} x$ is defined for all these numbers, can you say what the domain is?