**Sol 1** Let . Then , so and therefore
.

**Sol 2** Let . Then , so
and
. Thus
.

**Sol 3** Let , so and . Then
, so
. The domain of is the same
as the range of , so it is the interval

since the graph of f is the top half of the parabola .

**Sol 4** Let
. Then
, so

**Sol 5** Setting , for example, and then solving for gives
; so is not 1-1 and therefore does not have an inverse.

**Sol 6** Let ; then , so adding 4 to both sides gives
and therefore . Taking square roots of both sides,
using the fact that so , gives
and so
. Therefore
. The domain of
is the range of , which is the interval since
for .

**Sol 7** To find , we must solve the equation for :

since . Therefore .

**Sol 8** Let
.

Then

,

so .

The domain of is the same as the range of . Since for , for . Furthermore, if , then and therefore ; so the domain of is ,the range of .

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