Question

What is the domain of the rational function f of x is equal to the quantity x squared plus x minus 6 end quantity over the quantity x cubed minus 3 times x squared minus 16 times x plus 48 end quantity question mark

Answer 1

To solve this problem, we have to find the zeros of the expression in the denominator, to do it, factor the expression:

`\begin{gathered} x^3-3x^2-26x+48=0 \\ (x-3)(x-4)(x+4)=0 \\ x-3=0 \\ x=3 \\ x-4=0 \\ x=4 \\ x+4=0 \\ x=-4 \end{gathered}`

The zeros of the function are x=3,4,-4.

Since these values make the expression be zero, they are not included in the domain of the function. This is because the expression in the denominator can not be zero, otherwise, the function would be undefined.

The correct answer is B:

`\mleft\lbrace x\in R\mright|x\\e-4,3,4\}`