Domain Rational 239F9C

1. **State the problem:** We need to find the domain of the function $$f(x) = \frac{7 - 3x}{4x - 9}$$.\n\n2. **Recall the domain rule for rational functions:** The domain includes all real numbers except where the denominator is zero, because division by zero is undefined.\n\n3. **Set the denominator equal to zero and solve:**\n$$4x - 9 = 0$$\n\n4. **Solve for $$x$$:**\n$$4x = 9$$\n$$x = \frac{9}{4}$$\n\n5. **Interpretation:** The function is undefined at $$x = \frac{9}{4}$$.\n\n6. **Write the domain:** All real numbers except $$x = \frac{9}{4}$$. In interval notation, this is:\n$$(-\infty, \frac{9}{4}) \cup (\frac{9}{4}, \infty)$$\n\n**Final answer:** The domain of $$f$$ is all real numbers except $$x = \frac{9}{4}$$.