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

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