The functions are and .

To find , we need to find the domain of , which can be done for .

Solve the inequality .

Subtract  from each side

.

Then you must able to evaluate for each of these values, which can only be done for all real values. Since will always be positive.

Therefore, the domain of is all real numbers.

Find .

Replace with .

Substitute for in .

Notice that is only defined for , which is the same restriction determined the by considering the domains of and .

Therefore,   for .

To find , you must first be able to find , which can be done for .

Then evaluate for each of these values, which can only be done for all .

.

Substitute .

Since is defined only positive real numbers.

Square on both sides.

Combining the two restrictions.

Therefore, the domain of is .

Find

Replace with .

Substitute for in .

.

Notice that is only defined for .

Combine this restriction with the restriction . The true domain of is .

Therefore,   for .

  for ..

for .