Find the domain of the rational function.
-$$f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$$
A) all real numbers
B) $\{ x \mid x \neq - 3 , x \neq 5 \}$
C) $\{ x \mid x \neq 3 , x \neq - 3 , x \neq - 5 \}$
D) $\{ x \mid x \neq 3 , x \neq - 5 \}$

Question

Quizplus · Accepted Answer

The domain of a rational function is all real numbers except for the values that make the denominator zero. In this case, the denominator is $3x^2 + 6x - 45$, which factors as $3(x+5)(x-3)$. Therefore, the domain is all real numbers except for $x=-5$ and $x=3$.

Find the Domain of the Rational Function f(x)=2x2−43x2+6x−45f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }f(x)=3x2+6x−452x2−4​

Find the Domain of the Rational Function $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$