Determine the domain of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$.
A) all real numbers except $x = - 1 , x = 0$, and $x = 3$
B) all real numbers except $x = 0$ and $x = 3$
C) all real numbers except $x = - 3$ and $x = - 1$
D) all real numbers except $x = 3$
E) all real numbers

Question

Quizplus · Accepted Answer

The domain of $f(x) = \frac{3x + 3}{x^2 - 3x}$ is determined by the values of $x$ for which the denominator is not zero. Factoring the denominator gives $x(x - 3)$, which is zero when $x = 0$ or $x = 3$. Therefore, the domain excludes $x = 0$ and $x = 3$, making option B correct.

Determine the Domain Of f(x)=3x+3x2−3xf ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }f(x)=x2−3x3x+3​

Determine the Domain Of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$