# How do you find the domain and range of #f(x) = x/(x^2 +1)#?

##### 2 Answers

The domain of

and the range is

#### Explanation:

Solving for the domain of

By contemplating the output of our function, we will notice that, from the right the function is decreasing until the point

From either direction,

Therefore the highest point on our graph is

The domain is

#### Explanation:

The denominator is

The domain is

To find, the range procced as follows :

Let

In order for this quadratic equation to have solutions, the discriminant

Therefore,

The solution to this inequality is

The range is

graph{x/(x^2+1) [-3, 3.93, -1.47, 1.992]}