The functions are
and
.
:
All possible values of
is the domain of the function.
The denominator of the function should not be zero.
\
The domain of
is
.
:
All possible values of
is the domain of the function.
The domain of
is the set of all real numbers.
(a)
\Find
.

.
The domain of the inside function
is
.
All possible values of
is the domain of the function.
The denominator of the composite function should not be zero.
\
From general solution 

The domain of
is
.
(b)
\Find
.

.
The domain of the inside function
is
.
The composite function has no restrictions, so all possible values of
is the domain of the function.
The domain of
is
.
(c)
\Find
.

.
The domain of the inside function
is
.
All possible values of
is the domain of the function.
The denominator of the composite function should not be zero.
\
The domain of
is
.
(d)
\Find
.

.
The domain of the inside function
is
.
The composite function has no restrictions, so all possible values of
is the domain of the function.
The domain of
is
.
(a)
, and its domain is
.
(b)
, and its domain is
.
(c)
, and its domain is
.
(d)
, and its domain is
.