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.

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.