QuestionSuppose that $\mathrm{G}(\mathrm{x})=\log _{3}(2 \mathrm{x}+1)-2$. (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?

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