Find the domain & range of :f(x)= √((x-1) )
Answers
Step-by-step explanation:
The domain of the given function
f
(
x
)
is the set of input values for which
f
(
x
)
is real and defined.
Point to note:
√
f
(
x
)
=
f
(
x
)
≥
0
Solve for
(
x
−
1
)
≥
0
to obtain
x
≥
1
.
Hence,
Domain:
x
≥
1
Interval Notation:
[
1
,
∞
)
Step 2:
Range:
Range is the set of values of the dependent variable used in the function
f
(
x
)
for which
f
(
x
)
is defined.
Hence,
Range:
f
(
x
)
≥
0
Interval Notation:
[
0
,
∞
)
Step 3:
Additional note:
The function
y
=
f
(
x
)
=
√
x
−
1
has no asymptotes.
Create a data table using values for
x
and corresponding values for
y
:
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Observe that
Z
e
r
o
and
Negative values
of
x
make the function
f
(
x
)
undefined
at those points.
Graph
f
(
x
)
=
√
x
−
1
Answer:
Domain : x - 1 > 0
x > 1
Therefore, x€ [ 1, infinity )
Range: [ 0, infinity )