1. The problem asks for the domain of the function $$f(x) = \frac{7 - 3x}{4x - 9}$$. 2. The domain of a rational function is all real numbers except where the denominator is zero because division by zero is undefined. 3. Set the denominator equal to zero and solve for $$x$$: $$4x - 9 = 0$$ 4. Solve for $$x$$: $$4x = 9$$ $$x = \frac{9}{4}$$ 5. Therefore, the domain of $$f$$ is all real numbers except $$x = \frac{9}{4}$$. 6. In interval notation, the domain is: $$(-\infty, \frac{9}{4}) \cup (\frac{9}{4}, \infty)$$