Question
upstudy study bank question image url

Find the domain of the following rational function. \[ R(x)=\frac{x}{x^{3}+8} \]

Ask by Stephens Flynn. in the United States
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The domain of \( R(x) = \frac{x}{x^{3}+8} \) is all real numbers except \( x = -2 \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

To find the domain of the rational function \( R(x) = \frac{x}{x^3 + 8} \), we need to identify the values of \( x \) that make the denominator zero, as these values are excluded from the domain. Start by setting the denominator equal to zero: \[ x^3 + 8 = 0 \] This can be rewritten as: \[ x^3 = -8 \] Taking the cube root of both sides, we find: \[ x = -2 \] Thus, the function is undefined at \( x = -2 \). Therefore, the domain of \( R(x) \) includes all real numbers except \( -2 \). In interval notation, the domain is: \[ (-\infty, -2) \cup (-2, \infty) \]

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy