The functions are
and
.
Find
.
The sum
is the function defined by :
.
.
All possible values of
is domain of a function.
The function
is a rational function.
The denominator of the function should not be the zero.
\
Domain of
= domain of
domain of
.
The domain of
is all real numbers except
.

Find
.
The difference
is the function defined by :
.
.
All possible values of
is domain of a function.
The function
is a rational function.
The denominator of the function should not be the zero.
\
Domain of
= domain of
domain of
.
The domain of
is all real numbers except
.
Find
.
The product
is the function defined by :
.
.
All possible values of
is domain of a function.
The function
is a rational function.
The denominator of the function should not be the zero.
\
Domain of
= domain of
domain of
.
The domain of
is all real numbers except
.

Find
.
The quotient
is the function defined by :
.

.
All possible values of
is domain of a function.
The function
is a rational function.
The denominator of the function should not be the zero.
\
Domain of
=
domain of
domain of
.
The function
.
Since
is undefined when
.
So exclude
.
The domain of
is all real numbers except
and
.

Find
.
.
Substitute
in
.
.
\

Find
.
.
Substitute
in
.

.

Find
.
.
Substitute
in
.
.

Find
.
.
Substitute
in
.
.
, domain is all real numbers except
.
, domain is all real numbers except
.
, domain is all real numbers except
.
, domain is all real numbers except
and
.
.
.
.
.