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

Question

Look at the following function:

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

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

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

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

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

No, the entire domain