Question

Find the domain of the following piecewise function.

Answer 1

`(2,8]`

Explanation:

Given

The attached piece wise function

Required

The domain

To do this, we simply consider the inequalities that bound the values of x.

The inequalities are:

`2 < x < 4`
`4 < x < 8` and
`x \ge 8`

Combine the first two inequalities:

`2 < x < 8` and
`x \ge 8`

For the inequality to be true, we must have:

`2 < x \le 8`

In interval notation, the inequality is:

`(2,8]`