Find the domain of the following function using interval notation: f (x) = 3Vx — 2

To find the domain of the function \( f(x) = 3\sqrt{x - 2} \), we need to determine the set of values for \(x\) that make the function defined.

The square root function \( \sqrt{x - 2} \) is defined only when the expression inside the square root is non-negative. This means:

\[
x - 2 \geq 0
\]

Solving this inequality:

\[
x \geq 2
\]

So, the domain of the function is all \(x\) values greater than or equal to 2.

### Domain in Interval Notation

The domain in interval notation is:

\[
[2, \infty)
\]

### Conclusion

The domain of the function \( f(x) = 3\sqrt{x - 2} \) is \([2, \infty)\).

Would you like more details or have any questions? Here are 5 related questions to explore:

1. How do you find the domain of a function with both a square root and a rational expression?
2. What happens to the domain if the function is \( f(x) = 3\sqrt{x^2 - 4} \)?
3. How is the range of a function determined, and what is the range of \( f(x) = 3\sqrt{x - 2} \)?
4. How do you handle the domain of a logarithmic function like \( f(x) = \log(x - 2) \)?
5. How does the domain change if the function is \( f(x) = \sqrt{x^2 - 4} \)?

**Tip**: When finding domains, always consider restrictions like square roots (which require non-negative expressions) and denominators (which must not be zero).

Find the domain of the following function using interval notation: f(x) = 3√x - 2

Learn how to find the domain of the square root function f(x) = 3√x - 2 using interval notation. This step-by-step solution covers algebraic concepts and inequalities. Suitable for students in Grades 9-10.

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