The function, $f(x) = x-\frac{1}{x}$ is

increasing for all $x ∈ (-∞,0) ∪ (0,∞)$

The correct answer is Option (1) → increasing for all $x ∈ (-∞,0) ∪ (0,∞)$

Given: $f(x) = x - \frac{1}{x}$

Domain: $x \ne 0$

Compute derivative: $f'(x) = 1 + \frac{1}{x^2}$

Since $\frac{1}{x^2} > 0$ for all $x \ne 0$, $f'(x) > 0$ for all $x \ne 0$

So, $f(x)$ is increasing on both intervals $(-\infty, 0)$ and $(0, \infty)$ separately