Answer
(a) $x=\frac{cos^{-1}(y)}{3}$
(b) $x=cot^{-1}(\frac{y-4}{3})$
Work Step by Step
(a) If $x\in[0,\frac{\pi}{3}]$, then $3x\in[0,\pi]$. For $y=cos(3x)$ with $y\in[-1,1]$, we can find $3x=cos^{-1}(y)$ and $x=\frac{cos^{-1}(y)}{3}$
(b) From $y=4+3cot(x)$ with $x\in(0,\pi)$, we have $cot(x)=\frac{y-4}{3}$ and $x=cot^{-1}(\frac{y-4}{3})$
