Find the Domain of (5+4x)/(2+x²): Rational Function Analysis

Look at the following function:

5+4x2+x2 \frac{5+4x}{2+x^2}


Does the function have a domain? If so, what is it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:11 First, we need to know if the function has a domain. And if it does, what is it?
00:16 To find the domain, keep in mind that dividing by zero is not allowed.
00:21 So, let's figure out what value makes the denominator equal to zero.
00:26 Alright, let's try to isolate X to find that value.
00:31 Remember, any number squared is always greater than zero. That's positive.
00:36 And there you have it! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following function:

5+4x2+x2 \frac{5+4x}{2+x^2}


Does the function have a domain? If so, what is it?

2

Step-by-step solution

Since the denominator is positive for all x x , the domain of the function is the entire domain.

That is, all values of x x . Therefore, there is no domain limits.

3

Final Answer

No, the entire domain

Practice Quiz

Test your knowledge with interactive questions

\( 2x+\frac{6}{x}=18 \)

What is the domain of the above equation?

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