Find the domain and range of f(x) = | x-1| /x-1.
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Answer:
f
(
x
)
=
x
−
1
x
+
1
Set the denominator in
x
−
1
x
+
1
equal to
0
to find where the expression is undefined.
x
+
1
=
0
Subtract
1
from both sides of the equation.
x
=
−
1
The domain is all values of
x
that make the expression defined.
Interval Notation:
(
−
∞
,
−
1
)
∪
(
−
1
,
∞
)
Set-Builder Notation:
{
x
|
x
≠
−
1
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
(
−
∞
,
1
)
∪
(
1
,
∞
)
Set-Builder Notation:
{
y
|
y
≠
1
}
Determine the domain and range.
Domain:
(
−
∞
,
−
1
)
∪
(
−
1
,
∞
)
,
{
x
|
x
≠
−
1
}
Range:
(
−
∞
,
1
)
∪
(
1
,
∞
)
,
{
y
|
y
≠
1
}
image of graph
([)]
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