contestada

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?

Respuesta :

Given the function

[tex] \dfrac{\sqrt{x^2+1}}{x} [/tex]

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 [tex] x^2+1[/tex], which is always positive, so it's not a problem.

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

So, the domain of the function is

[tex] D = \{ x \in \mathbb{R}:\ x \neq 0\} [/tex]