Given f(x) =

 {9-x2,  x<2

{ √x +7, 2≤x<10 

{[x-4] ,x ≥ 10

(a) f(2)

To find \( f(2) \), we need to determine which part of the piecewise function \( f(x) \) applies when \( x = 2 \).

The function \( f(x) \) is defined as:

\[
f(x) = 
\begin{cases}
9 - x^2, & \text{if } x < 2 \\
\sqrt{x} + 7, & \text{if } 2 \leq x < 10 \\
|x - 4|, & \text{if } x \geq 10 
\end{cases}
\]

Since \( x = 2 \) falls in the interval \( 2 \leq x < 10 \), we use the second piece of the function:

\[
f(x) = \sqrt{x} + 7
\]

Now, plug in \( x = 2 \):

\[
f(2) = \sqrt{2} + 7
\]

\[
f(2) = \sqrt{2} + 7 \approx 1.414 + 7 = 8.414
\]

Therefore, \( f(2) = \sqrt{2} + 7 \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is \( f(10) \) for the given function?
2. How do you find \( f(x) \) for values less than 2?
3. What is the domain of the function \( f(x) \)?
4. How would you graph this piecewise function?
5. What are the intervals where \( f(x) \) is continuous?

**Tip:** When working with piecewise functions, always pay attention to the conditions for each piece to determine which part of the function to use for specific values of \( x \).

Understand how to calculate f(2) using a piecewise function definition. This problem involves evaluating different parts of the function based on the value of x. Suitable for Grades 10-12.

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