52.1k views
0 votes
Hello!I need some assistance with my homework questions. An image named HW 4 is posted below.

Hello!I need some assistance with my homework questions. An image named HW 4 is posted-example-1

1 Answer

4 votes

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,∞).

User Mayerling
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories