Determine the Domain of the Function: 20/√(4x-2)

Q: Why can't the expression under the square root equal zero?

When the expression under the square root equals zero, the entire denominator becomes zero. Since we can't divide by zero in mathematics, we must exclude this value from the domain.

Q: What's the difference between ≥ and > in domain problems?

Use ≥ when the square root is in the numerator (like $ \sqrt{4x-2} $). Use > when the square root is in the denominator because zero makes division undefined.

Q: How do I check if x = 1 is in the domain?

Substitute: $ \frac{20}{\sqrt{4(1)-2}} = \frac{20}{\sqrt{2}} $. Since √2 ≈ 1.41 (positive), x = 1 is valid!

Q: What happens if I try x = 0.5?

At x = 0.5: $ \sqrt{4(0.5)-2} = \sqrt{0} = 0 $. This makes the denominator zero, so the function is undefined at this point.

Q: Can x be negative in this function?

No! Try x = 0: $ 4(0) - 2 = -2 $. We can't take the square root of negative numbers in real numbers, so all negative values are excluded.

Domain of Functions with Square Root Denominators

Look at the following function:

$\frac{20}{\sqrt{4x-2}}$

What is the domain of the function?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Does the function have a domain? If so, what is it?

00:04 A root must be for a positive number greater than 0

00:10 Let's isolate X

00:26 Let's reduce numerator and denominator by 2

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following function:

$\frac{20}{\sqrt{4x-2}}$

What is the domain of the function?

Step-by-step solution

To solve the problem of finding the domain of the function $\frac{20}{\sqrt{4x-2}}$ , we need to ensure that the expression under the square root is non-negative, and that we do not divide by zero.

**Step 1:** Solve for when the expression inside the square root is non-negative:

$4x - 2 \geq 0$

Add 2 to both sides:

$4x \geq 2$

Divide both sides by 4:

$x \geq 0.5$

**Step 2:** Ensure the denominator is not zero:

$4x - 2 \neq 0$

From $4x - 2 = 0$ , we solve:

$4x = 2$

$x = 0.5$

Since at $x = 0.5$ , the denominator becomes zero, we exclude this point. Therefore, $x > 0.5$ .

Final Answer

$x > 0.5$

Key Points to Remember

Essential concepts to master this topic

Domain Rule: Expression under square root must be positive
Technique: Set 4x - 2 > 0, solve to get x > 0.5
Check: Test x = 1: √(4(1) - 2) = √2 is positive ✓

Common Mistakes

Avoid these frequent errors

Using ≥ instead of > for square root in denominator
Don't set 4x - 2 ≥ 0 to get x ≥ 0.5 = includes x = 0.5 where denominator is zero! This creates division by zero which is undefined. Always use strict inequality > to exclude the point where the denominator becomes zero.

Practice Quiz

Test your knowledge with interactive questions

$\frac{6}{x+5}=1$

What is the field of application of the equation?

FAQ

Everything you need to know about this question

Why can't the expression under the square root equal zero?

When the expression under the square root equals zero, the entire denominator becomes zero. Since we can't divide by zero in mathematics, we must exclude this value from the domain.

What's the difference between ≥ and > in domain problems?

Use ≥ when the square root is in the numerator (like $\sqrt{4x-2}$ ). Use > when the square root is in the denominator because zero makes division undefined.

How do I check if x = 1 is in the domain?

Substitute: $\frac{20}{\sqrt{4(1)-2}} = \frac{20}{\sqrt{2}}$ . Since √2 ≈ 1.41 (positive), x = 1 is valid!

What happens if I try x = 0.5?

At x = 0.5: $\sqrt{4(0.5)-2} = \sqrt{0} = 0$ . This makes the denominator zero, so the function is undefined at this point.

Can x be negative in this function?

No! Try x = 0: $4(0) - 2 = -2$ . We can't take the square root of negative numbers in real numbers, so all negative values are excluded.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime