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

Given the following function:

5+4x(x3)2 \frac{5+4x}{(x-3)^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 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

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the following function:

5+4x(x3)2 \frac{5+4x}{(x-3)^2}

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

2

Step-by-step solution

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.

3

Final Answer

Yes, x3 x\ne3

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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