*f*(*x*)=⎩⎨⎧​−2*x*+2−2*x*+5−(*x*−6)2−7​ for *x*≤211​ for 2<*x*<611​ for *x*≥611​​

Find , f, of, 4

Find *f*(4)

The function \( f(x) \) is given piecewise as:

\[
f(x) = 
\begin{cases} 
-2x + 2 & \text{for } x \leq 2 \\
-2x + 5 & \text{for } 2 < x < 6 \\
-(x - 6)^2 - 7 & \text{for } x \geq 6
\end{cases}
\]

To find \( f(4) \), we need to determine which piece of the function applies when \( x = 4 \).

Since \( 4 \) is between 2 and 6 (i.e., \( 2 < 4 < 6 \)), we use the second case:

\[
f(x) = -2x + 5
\]

Substitute \( x = 4 \):

\[
f(4) = -2(4) + 5 = -8 + 5 = -3
\]

Thus, \( f(4) = -3 \).

Would you like any further details or clarifications?

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Here are five related questions to further explore the topic:

1. What is \( f(2) \) using the same function?
2. What is the value of \( f(6) \)?
3. How do you find the domain and range of a piecewise function?
4. How do we graph the given piecewise function?
5. Can piecewise functions be continuous? If so, how can we check for continuity?

**Tip:** Always check the interval that corresponds to the input value when evaluating piecewise functions!

Find f(4) for the function f(x) defined as a piecewise function:

f(x) =
-2x + 2 for x ≤ 2
-2x + 5 for 2 < x < 6
-(x - 6)^2 - 7 for x ≥ 6

Learn how to evaluate the piecewise function f(x) and find f(4). The function is defined by three different expressions depending on the value of x. This problem is suitable for students in Grades 9-12 and covers key concepts in algebra.

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