So I'm preparing for my further studies (last year of high school, preparing so I can try and join the academy that I want), and just solving problems. Got stuck on this one:
Find the inverse of $$f(x)=\sin(3x-1)$$ in the domain of $x \in \left[\dfrac{2-\pi}{6}, \dfrac{2+\pi}{6}\right]$.
What I've tried so far is:
$f(x) = y\\y=\sin(3x-1)\\y = \sin(3x)\cos(1)-\cos(3x)\sin(1)$
At this point I have no idea what to do, I thought of trying to split $3x=2x+x$ and continuing but it would be too messy.