To find the x-intercept of the function $y = x - \frac{1}{x}$, we need to set $y = 0$ and solve for $x$.

So, solve:

$0 = x - \frac{1}{x}$

Multiply through by $x$ to eliminate the fraction:

$0 = x^2 - 1$

This simplifies to:

$x^2 = 1$

Taking the square root of both sides:

$x = \pm 1$

Thus, the x-intercepts are $x = 1$ and $x = -1$.

Summary:

The x-intercepts are at $x = 1$ and $x = -1$.

Would you like further details or have any questions?

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Here are five related questions for further practice:

1. What is the y-intercept of the function $y = x - \frac{1}{x}$?
2. How would you find the critical points of this function?
3. What is the behavior of the function as $x \to \infty$?
4. Can you sketch the graph of the function $y = x - \frac{1}{x}$?
5. How do you determine the asymptotes for this function?

Tip: When solving rational equations, multiplying through by a common denominator helps eliminate fractions.