QuestionSuppose that $G(x)=\log _{3}(2 x+1)-2$ (a) What is the domain of G ? (b) What is $\mathrm{G}(13)$ ? What point is on the graph of G ? (c) If $\mathrm{G}(\mathrm{x})=2$, what is x ? What point is on the graph of G ? (d) What is the zero of G ? (a) The domain of G is $\square$ . (Type your answer in interval notation.)

Studdy Solution
Solve for $x$:
$$2x = 9 - 1$$ $$2x = 8$$ $$x = 4$$
The zero of $G(x)$ is at $x = 4$.
(a) The domain of $G$ is $\boxed{(-\frac{1}{2}, \infty)}$.
(b) $G(13) = 1$. The point on the graph is $(13, 1)$.
(c) When $G(x) = 2$, $x = 40$. The point on the graph is $(40, 2)$.
(d) The zero of $G$ is at $x = 4$.