Find the domain of each of the following functions given by

Given:

To find: the domain of function

Explanation: So, the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

Given,

Now for real value of f,

x + |x|>0

Now when x>0,

x + |x|>0⇒ x + x>0⇒ 2x>0⇒ x>0

Now when x<0,

x + |x|>0⇒ x-x>0⇒ 2x>0⇒ x>0

This is not possible.

So, x>0, to satisfy the given equation.

Hence the domain of f = R ⁺