Question: f(x) = (7 - 3x)/(4x - 9) What is the domain of f? graph: linear function represented as a rational expression; position_hint = center

1. **Problem:** Find the domain of $f(x)=\frac{7-3x}{4x-9}$.\n\n2. **Formula/rule:** A rational function is undefined when its denominator is $0$.\nSo we set the denominator equal to $0$ and solve: $4x-9=0$.\n\n3. **Solve for the excluded value:**\n$$4x-9=0$$\n$$4x=9$$\n$$x=\frac{9}{4}$$\nSince we divided by $4$, there is no cancellation to show here.\n\n4. **Domain rule:** The domain is all real numbers except the value that makes the denominator $0$.\nSo $x=\frac{9}{4}$ must be excluded.\n\n5. **Answer:** The domain is $(-\infty,\frac{9}{4})\cup(\frac{9}{4},\infty)$.