Question

Use the drawing tools to form the correct answers on the grid.

Plot any discontinuities of the function f(x)= 1/(x^2+2)

Answer 1

The function
`f(x)= (1)/(x^2+2)` is continuous for all real numbers

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:

`x ^ 2 + 2`

Then we equal 0 and clear x

`x ^ 2 +2 = 0\\\\x ^ 2 = -2`

`x ^ 2> 0` for any real number.

This means that

`x ^ 2 +2> 0` for all reals numbers.

Therefore, the function
`f(x)= (1)/(x^2+2)` is continuous for all real numbers, that is, it does not have discontinuities.

The graphic of this function is shown in the image