1. **State the problem:** Find the domain and range of the function $$g(x) = \frac{6x - 2}{3x - 4}$$. 2. **Find the domain:** The domain consists of all real numbers except where the denominator is zero because division by zero is undefined. Set the denominator equal to zero: $$3x - 4 = 0$$ Solve for $x$: $$3x = 4$$ $$x = \frac{4}{3}$$ So, the domain is all real numbers except $x = \frac{4}{3}$. 3. **Find the range:** To find the range, set $y = g(x)$ and solve for $x$: $$y = \frac{6x - 2}{3x - 4}$$ Multiply both sides by the denominator: $$y(3x - 4) = 6x - 2$$ Distribute $y$: $$3xy - 4y = 6x - 2$$ Group terms with $x$ on one side: $$3xy - 6x = 4y - 2$$ Factor out $x$: $$x(3y - 6) = 4y - 2$$ Solve for $x$: $$x = \frac{4y - 2}{3y - 6}$$ For $x$ to be defined, the denominator cannot be zero: $$3y - 6 \neq 0$$ $$3y \neq 6$$ $$y \neq 2$$ Therefore, the range is all real numbers except $y = 2$. **Final answers:** - Domain: $$\{x \in \mathbb{R} \mid x \neq \frac{4}{3} \}$$ - Range: $$\{y \in \mathbb{R} \mid y \neq 2 \}$$