Find the Domain and Range f(x) = log of x-1+2
f
(
x
)
=
log
(
x
−
1
)
+
2
f(x)=log(x-1)+2
Set the argument in
log
(
x
−
1
)
log(x-1) greater than
0
0 to find where the expression is defined.
x
−
1
>
0
x-1>0
Add
1
1 to both sides of the inequality.
x
>
1
x>1
The domain is all values of
x
x that make the expression defined.
Interval Notation:
(
1
,
∞
)
(1,∞)
Set-Builder Notation:
{
x
|
x
>
1
}
{x|x>1}
The range is the set of all valid
y
y values. Use the graph to find the range.
Interval Notation:
(
−
∞
,
∞
)
(-∞,∞)
Set-Builder Notation:
{
y
|
y
∈
R
}
{y|y∈ℝ}
Determine the domain and range.
Domain:
(
1
,
∞
)
,
{
x
|
x
>
1
}
(1,∞),{x|x>1}
Range:
(
−
∞
,
∞
)
,
{
y
|
y
∈
R
}
(-∞,∞),{y|y∈ℝ}
