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
00:00 Does the function have a domain? And if so, what is it?
00:03 To find the domain, remember that division by 0 is not allowed
00:08 Therefore, let's see what solution makes the denominator zero
00:11 Let's isolate X
00:17 Any number squared is necessarily positive (greater than 0)
00:25 And this is the solution to the question

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

Given the following function:

\( \frac{5-x}{2-x} \)

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

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