Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$.
A) all real numbers except $x = - 1 , x = 0$, and $x = 6$
B) all real numbers except $x = 0$ and $x = 6$
C) all real numbers except $x = - 6$ and $x = - 1$
D) all real numbers except $x = 6$
E) all real numbers

Question

Quizplus · Accepted Answer

The function has a denominator of $x^2-6x$, which means it cannot be equal to zero. Thus, we need to exclude any value of $x$ that makes the denominator zero. Factoring the denominator gives: $x(x-6)$. Therefore, the function is undefined for $x=0$ and $x=6$. The function is also undefined at any value that makes the expression in the denominator negative (since we cannot take the square root of a negative number). This occurs when $x<0$ or when $x>6$. However, these values are already excluded because they make the denominator zero. Therefore, the only values that need to be excluded are $x=0$ and $x=6$, giving us a domain of all real numbers except $x=0$ and $x=6$.

Determine the Domain Of f(x)=6x+6x2−6xf ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }f(x)=x2−6x6x+6​

Determine the Domain Of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$