Find the domain of $$f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$$ .
A)all real numbers except x = 8 and x = -4
B)all real numbers
C)all real numbers except x = 4 and x = -8
D)all real numbers except x = -4,x = 4 and x = -8
E)all real numbers except x = -8

Question

Quizplus · Accepted Answer

The domain of a function is all the values of x for which the function is defined. For the given function, the denominator cannot be zero because division by zero is undefined. To find the values that are not in the domain, set the denominator equal to zero and solve for x: $x^2 + 4x - 32 = 0$. Factoring the quadratic equation, we get $(x + 8)(x - 4) = 0$, which gives the roots x = -8 and x = 4. Therefore, the function is undefined for x = -8 and x = 4, making the correct answer all real numbers except x = 4 and x = -8.

Find the Domain Of f(x)=x2−16x2+4x−32f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }f(x)=x2+4x−32x2−16​

Find the Domain Of $f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$