Chapter 1.3, Problem 3E

To determine

The points of discontinuity of the function. Identify the type of

Discontinuity.

Answer to Problem 3E

The function continuous everywhere and no point of discontinuity.

Explanation of Solution

Given:

  $y=\frac{1}{x^2+1}$

Calculation:

The given equation $y=\frac{1}{x^2+1}$ is polynomial.

Find the discontinuity point of the function $y=\frac{1}{x^2+1}$:

The domain of the expression is all real numbers except where the expression is

undefined.

In this case, there is no real number, that is the domain of the function is $\left(-\infty ,\infty \right)$ ,

that makes the expression undefined.

Thus, the function continuous everywhere and no point of discontinuity.