(a)
\The function are and
.
Find the domain of .
All possible values of x is the domain of the function.
\Since the function is a rational function, the denominator should not be the zero.
\Thus, the domain of the function is all possible values of x except
and 0.
Find the domain of .
Since it is a linear function, the domain is all real values of x.
\(b)
\The function .
Simplify the function.
\Since the function is a linear function, there is no vertical asymptote.
\(c)
\Completed table is :
\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
x \ | \
| ![]() |
\
| \
| ![]() |
\
| \
| ![]() |
\
| \
| ![]() |
\
0 \ | \
| 0 |
1 | \
| 1 |
2 | \
| 2 |
3 | \
| 3 |
(d)
\Observe the above table of values :
\The functional values of and
,
and
.
Thus, the function differ at , where f is undefined.
(a)
\The domain of the function is all possible values of x except
and 0.
The domain of is all real values of x.
(b)
\None.
\(c)
\Completed table is :
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
x \ | \
| ![]() |
\
| \
| ![]() |
\
| \
| ![]() |
\
| \
| ![]() |
\
0 \ | \
| 0 |
1 | \
| 1 |
2 | \
| 2 |
3 | \
| 3 |
(d) The functions f and g differ at , where f is undefined.