Question

Find the domain of the following piecewise function.

Answer 1

Answer:

$(2,8]$

Step-by-step 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:

$(2,8]$