https://file.aiquickdraw.com/mathbot/file/17296969174594kq82m1j.jpg

The image contains a mathematical problem in Persian. It presents a function machine where the function \( f(x+2) = \frac{x+1}{2} \) is defined. The question asks to calculate the value of \( f(2) + f(-2) \), and the possible answers are given: 0, -1, 1, -2, 3, 4.

### Let's solve it step by step:

#### 1. Calculate \( f(2) \):
The function given is \( f(x+2) = \frac{x+1}{2} \). To calculate \( f(2) \), we need to figure out for which \( x \), \( x+2 = 2 \).

- Solve: \( x+2 = 2 \) → \( x = 0 \).

Now, substitute \( x = 0 \) into the function:

\[
f(2) = f(x+2) = \frac{0+1}{2} = \frac{1}{2}
\]

#### 2. Calculate \( f(-2) \):
For \( f(-2) \), solve \( x+2 = -2 \):

- Solve: \( x+2 = -2 \) → \( x = -4 \).

Now, substitute \( x = -4 \) into the function:

\[
f(-2) = f(x+2) = \frac{-4+1}{2} = \frac{-3}{2}
\]

#### 3. Sum \( f(2) + f(-2) \):
Now, add the two results together:

\[
f(2) + f(-2) = \frac{1}{2} + \frac{-3}{2} = \frac{-2}{2} = -1
\]

### Final Answer:
The correct answer is \( -1 \), which corresponds to option 2 in the image.

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Would you like more details or have any further questions?

Here are 5 related questions to consider:
1. What is the general process to solve functional equations like this?
2. How does shifting the argument of a function affect its calculation?
3. Could this function be defined differently for non-integer values of \( x \)?
4. How would the solution change if the function were modified?
5. How can you graphically interpret the function transformation?

**Tip:** Always isolate the variable first when solving equations involving shifted arguments.

ماشین مقابل مربوط به تابع f است. حاصل f(2) + f(-2) کدام است؟

Learn how to solve the function equation f(2) + f(-2) using the formula f(x+2) = (x+1)/2. This step-by-step solution involves substituting values and performing arithmetic operations. Suitable for students in Grades 8-10.

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