Question

Hello!I need some assistance with my homework questions. An image named HW 4 is posted below.

Answer 1

Answer: (-∞,0)∪(0,∞)

Given:

`F(x)=(x-9)/(x^3+6x)`

First, we need to find the restrictions for this given function. That would be: the denominator shall not be equal to 0.

With that, we will equate the denominator to 0 to find the value of x in which the function is undefined.

`\begin{gathered} x^3+6x=0 \\ x(x^2+6)=0 \\ x=0 \\ -------- \\ x^2+6=0 \\ x^2=-6 \\ x=\pm\sqrt[]{-6} \end{gathered}`

With this, we now know that the x value should be equal to 0. Since ±√-6 is an imaginary number, we can ignore this result.

Therefore, the domain for the given function is (-∞,0)∪(0,∞).