whats the domain and range of $$ f\left(x\right)=\sqrt{x^2} $$

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.

whats the domain and range of f(x)=sqrt(x^2)?

Discover how to find the domain and range of f(x) = sqrt(x^2). Learn why it simplifies to the absolute value function f(x) = |x|, with a detailed explanation on domains of real numbers and ranges of non-negative values. Suitable for Grades 9-12.

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