`A={-2,-1,1,2}` and `f={(x,(1)/(x)),x inA}`
Is f a function?

Answer

To determine whether \( f \) is a function, we need to analyze the given set \( A \) and the relation defined by \( f \).

### Step-by-Step Solution:

1. **Identify the Set \( A \)**:
The set \( A \) is given as:
\[ A = \{-2, -1, 1, 2\} \]

2. **Define the Relation \( f \)**:
The relation \( f \) is defined as:
\[ f = \{(x, \frac{1}{x}) \mid x \in A\} \]
This means for each element \( x \) in set \( A \), we will find the corresponding value \( \frac{1}{x} \).

3. **Calculate the Values of \( f \)**:
We will compute \( \frac{1}{x} \) for each element in \( A \):
- For \( x = -2 \):
\[ f(-2) = \frac{1}{-2} = -\frac{1}{2} \]
- For \( x = -1 \):
\[ f(-1) = \frac{1}{-1} = -1 \]
- For \( x = 1 \):
\[ f(1) = \frac{1}{1} = 1 \]
- For \( x = 2 \):
\[ f(2) = \frac{1}{2} = \frac{1}{2} \]

4. **List the Pairs in Relation \( f \)**:
Now we can write the relation \( f \) as:
\[ f = \{(-2, -\frac{1}{2}), (-1, -1), (1, 1), (2, \frac{1}{2})\} \]

5. **Check the Definition of a Function**:
A relation is a function if every element in the domain (set \( A \)) is associated with exactly one element in the codomain. Here, we have:
- Each element of \( A \) maps to a unique value in the output.
- No element in \( A \) maps to more than one value.

6. **Conclusion**:
Since every element in \( A \) has a unique corresponding value in \( f \), we conclude that:
\[ f \text{ is a function.} \]

### Final Answer:
Yes, \( f \) is a function.

---