Answer:
The function [tex]f(x)= \frac{1}{x^2+2}[/tex] is continuous for all real numbers
Step-by-step explanation:
To know the possible points of discontinuity of this function, we must find out when the denominator of the function is equal to 0.
The denominator is:
[tex]x ^ 2 + 2[/tex]
Then we equal 0 and clear x
[tex]x ^ 2 +2 = 0\\\\x ^ 2 = -2[/tex]
[tex]x ^ 2> 0[/tex] for any real number.
This means that
[tex]x ^ 2 +2> 0[/tex] for all reals numbers.
Therefore, the function [tex]f(x)= \frac{1}{x^2+2}[/tex] is continuous for all real numbers, that is, it does not have discontinuities.
The graphic of this function is shown in the image
