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

Question

Quizplus · Accepted Answer

The denominator cannot be zero, so we need to solve $3x^2 + 6x - 45 = 0$. Factoring, we get $(3x - 9)(x + 5) = 0$, so $x = 3$ or $x = -5$. Therefore, the domain is all real numbers except $x = 3$ and $x = -5$.

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 $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$