Answer
$(\frac{2\pi}{3}, -\frac{3}{2})$ and $(\frac{4\pi}{3}, -\frac{3}{2})$; see graph.
Work Step by Step
Step 1. Graph $f(x)$ (red curve) and $g(x)$ (blue curve) as shown in the figure.
Step 2. Let $f(x)=g(x)$; we have $3cos(x)=cos(x)-1$ or $cos(x)=-\frac{1}{2}$ which gives solutions in $[0,2\pi]$ as $x=\frac{2\pi}{3}$ and $x=\frac{4\pi}{3}$ corresponding to points of intersection $(\frac{2\pi}{3}, -\frac{3}{2})$ and $(\frac{4\pi}{3}, -\frac{3}{2})$
Step 3. We can identify the above points as shown on the graph.
