Let f(x) be a continuous function defined for ` AA x in R ` , if f(x) take rational values ` AA x in R and f(2) = 198`, then ` f(2^(2))` = ……

Answer

To solve the problem, we need to analyze the given conditions about the function \( f(x) \).

### Step-by-Step Solution:

1. **Understanding the Function**:
The function \( f(x) \) is continuous for all \( x \in \mathbb{R} \) and takes only rational values. We are given that \( f(2) = 198 \).

2. **Applying the Properties of Continuous Functions**:
According to a concept in number theory, if a function is continuous and takes only rational values, it must be constant. This is because between any two rational numbers, there exists at least one irrational number. If the function were not constant, it would have to take on irrational values at some points due to its continuity.

3. **Conclusion about the Function**:
Since \( f(x) \) is continuous and takes only rational values, we conclude that \( f(x) \) must be a constant function. Therefore, for any \( x \), \( f(x) = c \) for some constant \( c \).

4. **Finding the Constant Value**:
We know that \( f(2) = 198 \). Since \( f(x) \) is constant, it follows that:
\[ f(x) = 198 \quad \text{for all } x \in \mathbb{R} \]

5. **Calculating \( f(4) \)**:
Now, we need to find \( f(4) \):
\[ f(4) = 198 \]

### Final Answer:
\[ f(4) = 198 \]