The function you provided is $f(x) = \sqrt{x^2}$.

Let's simplify the function: $f(x) = \sqrt{x^2} = |x|$ Here, $|x|$ represents the absolute value of $x$.

Domain:

The domain of $f(x) = |x|$ is the set of all real numbers since you can take the absolute value of any real number. Therefore, the domain is: $\text{Domain} = (-\infty, \infty)$

Range:

The range of $f(x) = |x|$ consists of all non-negative real numbers because the absolute value of any real number is always greater than or equal to zero. Therefore, the range is: $\text{Range} = [0, \infty)$

Final Answer:

• Domain: $(-\infty, \infty)$
• Range: $[0, \infty)$

Would you like more details or further explanation on this topic?

Here are 5 related questions you can explore:

1. What is the domain and range of $f(x) = |x + 2|$?
2. How do you find the domain and range of a square root function?
3. How does the domain change for $f(x) = \sqrt{x^2 - 4}$?
4. What is the domain and range of $f(x) = \sqrt{x^4}$?
5. How do transformations affect the range of a function?

Tip: When simplifying square roots of squares, always remember that $\sqrt{x^2} = |x|$, not just $x$. This avoids missing solutions in functions involving absolute values.