Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }$ .
A)Domain: all real numbers except x = -3 and 1
B)Domain: all real numbers except x = 1
C)Domain: all real numbers except x = -3 and -1
D)Domain: all real numbers except x = 3 and 1
E)Domain: all real numbers

Question

Quizplus · Accepted Answer

The domain of $f(x)$ is all real numbers except those that make the denominator equal to zero. Factoring the denominator gives $x^2 + 4x + 3 = (x + 3)(x + 1)$, so the values that are not in the domain are $x = -3$ and $x = -1$, because these values would make the denominator zero, causing the function to be undefined.

Determine the Domain of the Function f(x)=x2−9x2+4x+3f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }f(x)=x2+4x+3x2−9​

Determine the Domain of the Function $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }$