Evaluate the piecewise function at f (-1)
{x2-2
x <2
f(x) =
14+12-5|
x > 2

Let's evaluate the given piecewise function at \( f(-1) \).

The function is defined as:

\[
f(x) =
\begin{cases} 
x^2 - 2 & \text{if } x < 2 \\
14 + |12 - 5| & \text{if } x > 2 
\end{cases}
\]

To evaluate \( f(-1) \), we first determine which piece of the function applies. Since \( -1 < 2 \), we use the first case of the function:

\[
f(x) = x^2 - 2
\]

Substituting \( x = -1 \):

\[
f(-1) = (-1)^2 - 2 = 1 - 2 = -1
\]

Thus, \( f(-1) = -1 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you evaluate \( f(3) \) using the given piecewise function?
2. What is the definition of a piecewise function?
3. Can you graph this piecewise function to show its behavior?
4. What is the domain of this piecewise function?
5. How would the function change if the condition for \( x = 2 \) was included?

**Tip:** When evaluating piecewise functions, always check the condition first to determine which part of the function to use.

Evaluate the piecewise function at f(-1)
{x^2 - 2, x < 2 
14 + |12 - 5|, x > 2}

Learn how to evaluate the piecewise function at f(-1). This detailed explanation walks through the steps of applying conditions for piecewise functions, quadratic equations, and absolute value expressions. Ideal for students in Grades 9-10.

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