The function \( g(x) \) is defined piecewise, meaning that it has two different expressions depending on the value of \( x \). The function is given as:

\[
g(x) = 
\begin{cases} 
x + 5 & \text{for } x \leq 4 \\
9 - x & \text{for } x > 4 
\end{cases}
\]

To find \( g(-1) \), we need to determine which part of the piecewise function applies when \( x = -1 \).

Since \( -1 \leq 4 \), we use the first expression:

\[
g(x) = x + 5
\]

Now substitute \( x = -1 \) into the equation:

\[
g(-1) = -1 + 5 = 4
\]

Thus, \( g(-1) = 4 \).

Would you like a detailed explanation on piecewise functions or have any questions?

Here are 5 related questions:
1. How do you evaluate a piecewise function for different values of \( x \)?
2. What are the conditions under which each part of a piecewise function is used?
3. How do you graph a piecewise function like \( g(x) \)?
4. How would you find the domain of a piecewise function?
5. What happens when you input values exactly at the boundary of a piecewise function?

**Tip:** When working with piecewise functions, always carefully check which condition applies for the given value of \( x \).

Discover how to evaluate the piecewise function g(x), defined by two different expressions based on the value of x, at x = -1. This solution walks through which part of the function applies and provides a detailed breakdown. Ideal for high school students studying piecewise functions.

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