If the relation `f(x)={(1",",x in Q),(2",",x notin Q):}` where Q is set of rational numbers, then find the value `f(pi)+f((22)/(7))`.

Explanation

To solve the problem, we need to evaluate the function \( f(x) \) at two specific points: \( \pi \) and \( \frac{22}{7} \).

### Step-by-step Solution:

1. **Understand the function**: The function \( f(x) \) is defined as follows:
- \( f(x) = 1 \) if \( x \) is a rational number (i.e., \( x \in Q \)).
- \( f(x) = 2 \) if \( x \) is an irrational number (i.e., \( x \notin Q \)).

2. **Evaluate \( f(\pi) \)**:
- The number \( \pi \) is known to be an irrational number. Therefore, according to the definition of the function:
\[ f(\pi) = 2 \]

3. **Evaluate \( f\left(\frac{22}{7}\right) \)**:
- The number \( \frac{22}{7} \) is a rational number because it can be expressed as a fraction of two integers (22 and 7). Thus, according to the definition of the function:
\[ f\left(\frac{22}{7}\right) = 1 \]

4. **Calculate \( f(\pi) + f\left(\frac{22}{7}\right) \)**:
- Now, we can add the two values we have found:
\[ f(\pi) + f\left(\frac{22}{7}\right) = 2 + 1 = 3 \]

### Final Answer:
The value of \( f(\pi) + f\left(\frac{22}{7}\right) \) is \( 3 \).

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