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).