f(x)={ −x+5 ∣x−4∣ ​ for x<2 for x≥2 ​

It seems like you're defining a piecewise function \( f(x) \). Let's rewrite it clearly:

\[
f(x) = 
\begin{cases} 
-x + 5 & \text{for } x < 2 \\
x - 4 & \text{for } x \geq 2 
\end{cases}
\]

This means that the function behaves differently depending on the value of \( x \):

- **When \( x \) is less than 2**: The function is defined as \( f(x) = -x + 5 \).
- **When \( x \) is greater than or equal to 2**: The function is defined as \( f(x) = x - 4 \).

Would you like to see how to graph this function, find its domain and range, or any other details?

Here are some follow-up questions you might find helpful:

1. What is the graph of this piecewise function?
2. How do you find the domain and range of the function?
3. What is the value of \( f(x) \) at \( x = 2 \)?
4. How does the function behave as \( x \) approaches 2 from the left and right?
5. Can we find the points of intersection with the x-axis?

**Tip:** When dealing with piecewise functions, carefully check the conditions for each piece to understand the overall behavior of the function.

Explore the piecewise function f(x) = -x + 5 for x < 2 and f(x) = x - 4 for x >= 2. Learn about its definition, behavior at critical points, and how to interpret its graph. Suitable for high school students studying functions and calculus.

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