State the domain and range of $$ g(x)=\frac{-3}{x-6}+2 $$. The domain is all real numbers except $$ \square $$ and the range is all real numbers except

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For the function $$ g(x) = \frac{-3}{x-6} + 2 $$:

**Domain:**
The domain consists of all real numbers except where the denominator is zero. Set the denominator equal to zero and solve for $$ x $$:

$$
x - 6 \neq 0 \implies x \neq 6
$$

**Range:**
To find the range, consider the output $$ y $$ of the function:

$$
y = \frac{-3}{x-6} + 2
$$

Solve for $$ x $$ in terms of $$ y $$:

$$
y - 2 = \frac{-3}{x-6} \implies x - 6 = \frac{-3}{y - 2} \implies x = 6 - \frac{3}{y - 2}
$$

This equation is valid for all $$ y $$ except when $$ y - 2 = 0 $$, which would make the denominator zero. Therefore, $$ y $$ cannot be 2.

**Summary:**
- **Domain:** All real numbers except $$ 6 $$.
- **Range:** All real numbers except $$ 2 $$.

**Final Answer:**
The domain is all real numbers except 6 and the range is all real numbers except 2.
The domain is all real numbers except 6, and the range is all real numbers except 2.

State the domain and range of \( g(x)=\frac{-3}{x-6}+2 \). The domain is all real numbers except \( \square \) and the range is all real numbers except

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