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What are the horizontal asymptotes of the function f of x equals the quotient of the square root of the quantity x squared plus 1 and x?

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Given the function


(√(x^2+1))/(x)

The two points concerning the domain are:

  • The content of a square root must be non-negative
  • The denominator can't be zero

Nevertheless, the content of the square root is
x^2+1, which is always positive, so it's not a problem.

The denominator, which is x, can't be zero, so we can't have
x = 0

So, the domain of the function is


D = \{ x \in \mathbb{R}:\ x \\eq 0\}

User Robert Almgren
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