Calculus with Applications (10th Edition)

The domain is $\{(-\infty,\infty) \cap (-\infty , 3) \}= (-\infty , 3)$ .
$$f(x)=\sqrt{\frac{x^{2}}{3-x}}$$ the values $x$ for $f(x)$ is defined when: $$x^{2} \geq 0 \quad \text {and} \quad (3-x) \gt 0$$ $\Rightarrow$ $$-\infty \lt x \lt \infty \quad \text {and} \quad x \lt 3$$ since the radical cannot be negative and the denominator of the function cannot be zero. So we can observe that only values in the intervals $(-\infty, 3)$ satisfy the inequality. So the domain is $(-\infty,\infty) \cap (-\infty , 3) = (-\infty , 3)$ .