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 $\mathrm{G}$ ?

Answer

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Answer

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

Steps

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.

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 $\mathrm{G}$ ?

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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 $\mathrm{G}$ ?