X2/|x| +1

If you mean f(x) = x^2/|x| + 1, this simplifies for x ≠ 0 to |x| + 1. - For x > 0: f(x) = x + 1 - For x < 0: f(x) = -x + 1 - Domain: x ≠ 0 - Range: (1, ∞) Other notes: - lim as x → 0 of f(x) = 1 - Derivative: f'(x) = 1 for x > 0; f'(x) = -1 for x < 0; not differentiable at x = 0 - If you want a continuous extension, you could define f(0) = 1, which makes f(x) = |x| + 1 for all x Would you like a quick sketch, or help with limits, derivatives, or an integral?