Suppose that $G(x)=\log _{2}(2 x+2)-2$ (a) What is the domain df G? (b) What is $G(3)$ ? What point is on the graph of $G$ ? (c) If $G(x)=2$, what is $x$ ? What point is on the graph of $G$ ? (d) What is the zero of $\mathrm{G}$ ?

Step 1 ：In order for the given function to have a real value, the argument of the logarithm, i.e., $2x+2$, must be greater than 0. So, we have $2x+2>0$.

Step 2 ：Solving the inequality, we subtract 2 from both sides to get $2x>-2$.

Step 3 ：Then, we divide both sides by 2 to get $x>-1$.

Step 4 ：So, the domain of $G(x)$ is $x \in \boxed{(-1, \infty)}$ in interval notation.