Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$.
A) Domain: all real numbers except $x = - 4$ and 3
B) Domain: all real numbers except $x = - 16$
C) Domain: all real numbers except $x = - 4$ and $- 3$
D) Domain: all real numbers except $x = 4$ and 3
E) Domain: all real numbers

Question

Quizplus · Accepted Answer

The denominator $x^2 + 16$ cannot be zero because it is always positive for all real x (since $x^2$ is always non-negative and adding 16 ensures it's always positive). Therefore, the function is defined for all real numbers.

Determine the Domain of the Function f(x)=x2+7x+12x2+16f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }f(x)=x2+16x2+7x+12​

Determine the Domain of the Function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$