https://file.aiquickdraw.com/mathbot/file/1726363645981g7gy05i9.jpg

The question asks about a function \( f \) that satisfies the following conditions:

\[
f(1) = 2023 \quad \text{and} \quad f(x+1) + 2 = f(x) \quad \text{for every real number} \, x.
\]

We are asked to find the value of \( f(2) \).

### Step-by-step solution:

1. The recursive relation given is:
   \[
   f(x+1) = f(x) - 2
   \]
   This means that the value of the function decreases by 2 when \( x \) increases by 1.

2. From the condition \( f(1) = 2023 \), we can calculate \( f(2) \):
   \[
   f(2) = f(1+1) = f(1) - 2 = 2023 - 2 = 2021.
   \]

Therefore, the value of \( f(2) \) is \( \boxed{2021} \), which corresponds to option **A**.

Would you like further clarification or details on this solution?

Here are five related questions for practice:
1. If \( f(1) = 100 \), what is the value of \( f(3) \) given the same recursive relation?
2. What is the general formula for \( f(x) \) given the recursive relation \( f(x+1) + 2 = f(x) \)?
3. How would the solution change if the recursive relation was \( f(x+1) + 3 = f(x) \)?
4. What is the value of \( f(0) \) if \( f(1) = 2023 \)?
5. If \( f(x+1) = f(x) - 2 \), what is \( f(x) \) for large values of \( x \)?

**Tip:** Recursive relations can be solved step-by-step, but identifying a pattern can help you create a general solution.

Diketahui f adalah fungsi yang memenuhi f(1) = 2023 dan f(x+1) + 2 = f(x) untuk setiap bilangan real x. Nilai dari f(2) = ...

Solve the recursive function problem f(x+1) = f(x) - 2 with f(1) = 2023. Find the value of f(2) using step-by-step reasoning. This problem covers recursion and functional equations, suitable for Grades 10-12.

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