For the function \( f(x) = x - \frac{1}{x} \), we are asked to evaluate \( f(0) \) given a point \( (0, 5) \).

### Issue:

When \( x = 0 \), the function includes the term \( \frac{1}{x} \), which results in \( \frac{1}{0} \), and division by zero is **undefined** in mathematics. Therefore, **\( f(0) \) does not exist** for this function.

### Conclusion:
The point \( (0, 5) \) cannot be part of the curve for the function \( f(x) = x - \frac{1}{x} \) because the function is not defined at \( x = 0 \). This confirms that \( f(x) \) has a **domain of \( \mathbb{R} \setminus \{0\} \)**, meaning \( x = 0 \) is excluded.

Would you like further clarification on how division by zero impacts the domain? Here are 5 related questions:

1. What happens to the function \( f(x) = x - \frac{1}{x} \) near \( x = 0 \)?
2. How can vertical asymptotes help understand where a function is undefined?
3. Can we modify the function to include \( x = 0 \) in the domain?
4. What are the general rules for determining the domain of a rational function?
5. How does the graph of \( f(x) = x - \frac{1}{x} \) behave around \( x = 0 \

Learn why the function f(x) = x - 1/x is undefined at x = 0 due to division by zero. This problem explores key concepts like rational functions and the domain of functions, focusing on the exclusion of x = 0. Suitable for students in Grades 10-12.

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