Sales Toll Free No: 1-800-481-2338

How to Find Open Intervals of A Function?

TopEvery function has a Domain which contains the values at which the function is defined. The domain can be called as a collection of various closed and open intervals. If the interval is closed then it is represented as: [x, y] and if it is open then we write it as: (x, y). An interval can be closed – opened like [x, y) and opened – closed(x, y]. We generally define a function not defined at critical points by finding their Derivatives. So, let us learn how to find open intervals of a function.

Example: Suppose we have a function x2 + 4 x + 3 < 0. Find its domain?

Solution: In the function we have a less than inequality. We have to keep in consideration this inequality as:

x2 + 4 x + 3 < 0

or x2 + 3 x + x + 3 < 0,

or x (x + 3) + (x + 3) < 0,

or (x + 1) (x + 3) < 0,

Now there can be two possibilities as follows:

Either x < -1 and x < - 3 or x > -1 and x > - 3

If we take the first case x < -1 and x < - 3 we get the domain as:

'x' belongs to: Intersection ((- infinity, -1), (- infinity, -3)) = (- infinity, -3) in open intervals and

If we take the second case x > -1 and x > - 3 we get the domain as:

'x' belongs to: Intersection ((-1, infinity), (-3, infinity)) = (-1, infinity) in open intervals.

Thus the open intervals of the function x2 + 4 x + 3 < 0 are defined as: (- infinity, -3) or (-1, infinity).
These open intervals means that the value of the function is not defined at x = -infinity, -3, 1 and infinity.