Find the Domain of (5+4x)/(x-3)²: Rational Function Analysis

Question

Given the following function:

$\frac{5+4x}{(x-3)^2}$

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 we cannot divide by 0

00:06 So let's see what solution zeroes the denominator

00:09 We'll take the root to get rid of the exponent

00:20 Let's isolate X

00:27 And this is the solution to the question

When we have an unknown in a fraction, we immediately know that the domain must exclude where the denominator equals 0.

Therefore, we need to check in which case the denominator can become 0.

Let's set:

(x-3)²≠0

Let's take the square root of both sides:

x-3≠0

Let's isolate x:

x≠3

And this is the solution we were looking for, X cannot be 3, because then it wouldn't satisfy the domain we found.

Yes, $x\ne3$