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 expression is undefined for values of x that make the denominator zero since division by zero is undefined. Therefore, we must exclude the values of x that make the denominator zero.

To find these values, we set the denominator equal to zero and solve for x:

$$x^2 - 3x = 0$$
$$x(x-3) = 0$$
$$x = 0	ext{ or }x = 3$$

Therefore, the domain of f(x) is all real numbers except x = 0 and x = 3. The correct choice is B.

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 $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$